\letter {}
  (Near-)Additive Magma Categories, \indexit{551}
  (Near-)Additive Magma Generation, \indexit{552}
  `+', 48
  `-', 48
  `-A', 30
  `-B', 30
  `-C', 30
  `-D', 30
  `-K', 28
  `-L', 29
  `-M', 30
  `-N', 30
  `-O', 30
  `-P', 30
    \sub on Macintosh, 31
  `-R', 29
  `-T', 30
  `-U', 30
  `-W', 30
    \sub on Macintosh, 31
  `-X', 30
  `-Y', 30
  `-a', 29
    \sub on Macintosh, 31
  `-b', 27
  `-e', 27
    \sub on Macintosh, 31
  `-f', 27
    \sub on Macintosh, 31
  `-g', 28
  `-g -g', 28
  `-h', 27
  `-i', 30
  `-l', 29
  `-m', 28
  `-n', 27
    \sub on Macintosh, 31
  `-o', 28
    \sub on Macintosh, 31
  `-q', 27
  `-r', 29
  `-x', 28
  `-y', 28
  `-z', 30
    \sub on Macintosh, 31
  `.gaprc', 33
  `/', 48
    \sub for character tables, 725
  `\*', 48
    \sub for character tables, 725
  `\\\char 39', 248
  `\\XYZ', 248
  `\\\"', 248
  `\\\\', 248
  `\\b', 248
  `\\c', 248
  `\\in', operation for testing membership, 273
  `\\n', 248
  `\\r', 248
  `{\accent 94 }', 48
    \sub for class functions, 763
  1-Cohomology, \indexit{375}
  2-Cohomology and Extensions, \indexit{454}
\letter A
  `AbelianGroup', 505
  `AbelianInvariants', for character tables, 727
    \sub for groups, 364
  Abelian Invariants for Subgroups, \indexit{473}
  `AbelianInvariantsMultiplier', 378
  `AbelianInvariantsNormalClosureFpGroup', 474
  `Abelian\-Invariants\-Normal\-Closure\-Fp\-Group\-Rrs', 474
  `AbelianInvariantsOfList', 240
  `AbelianInvariantsSubgroupFpGroup', 473
  `AbelianInvariantsSubgroupFpGroupMtc', 473
  `AbelianInvariantsSubgroupFpGroupRrs', 474
  `AbelianNumberField', 583
  abelian number field, 585
  abelian number fields, canonicalbasis, 586
  abelian number fields, Galois group, 588
  `AbelianSubfactorAction', 400
  About Group Actions, \indexit{392}
  `AbsInt', 127
  `AbsoluteIrreducibleModules', 744
  `AbsoluteValue', 157
  absolute value of an integer, 127
  `AbsolutIrreducibleModules', 744
  abstract word, 322
  `AbstractWordTietzeWord', 482
  accessing, list elements, 172
    \sub record elements, 259
  Accessing a Module, \indexit{689}
  Accessing Record Elements, \indexit{259}
  Accessing Subgroups via Tables of Marks, \indexit{710}
  `AClosestVectorCombinationsMatFFEVecFFE', 216
  `AClosest\-Vector\-Combinations\-Mat\-FFEVec\-FFECoords', 216
  `ActingAlgebra', 626
  `ActingDomain', 404
  Acting OnRight and OnLeft, \indexit{430}
  `Action', 399
  action, by conjugation, 393
    \sub on blocks, 393
    \sub on sets, 393
  `ActionHomomorphism', 398
  Action of a group on itself, \indexit{400}
  Action on Subfactors Defined by a Pcgs, \indexit{445}
  actions, 393
  Actions of Matrix Groups, \indexit{426}
  `ActorOfExternalSet', 406
  `Add', 175
  add, an element to a set, 194
  `AddCoeffs', 214
  `AddGenerator', 484
  `AddGenerators', 341
  `AddGeneratorsExtendSchreierTree', 422
  addition, 48
    \sub list and non-list, 183
    \sub matrices, 220
    \sub matrix and scalar, 220
    \sub operation, 293
    \sub rational functions, 662
    \sub scalar and matrix, 220
    \sub scalar and matrix list, 222
    \sub scalar and vector, 212
    \sub vector and scalar, 212
    \sub vectors, 212
  Additive Arithmetic for Lists, \indexit{183}
  `AdditiveInverse', 291
  `AdditiveInverseAttr', 291
  `AdditiveInverseImmutable', 291
  `AdditiveInverseMutable', 291
  `AdditiveInverseOp', 291
  `AdditiveInverseSameMutability', 291
  `AdditiveInverseSM', 291
  `AdditiveNeutralElement', 553
  `AddRelator', 484
  `AddRowVector', 214
  `AddRule', 341
  `AddRuleReduced', 341
  `AddSet', 194
  `AdjointAssociativeAlgebra', 643
  `AdjointBasis', 615
  `AdjointMatrix', 643
  `AdjointModule', 628
  Advanced Features of GAP, \indexit{29}
  Advanced List Manipulations, \indexit{202}
  Advanced Methods for Dixon-Schneider Calculations, \indexit{745}
  `AffineAction', 445
  `AffineActionLayer', 445
  `AffineOperation', 445
  `AffineOperationLayer', 445
  `Agemo', 361
  `Algebra', 606
  `AlgebraByStructureConstants', 609
  `AlgebraGeneralMappingByImages', 620
  `AlgebraHomomorphismByImages', 620
  `AlgebraHomomorphismByImagesNC', 620
  `AlgebraicExtension', 683
  `AlgebraWithOne', 606
  `AlgebraWithOneGeneralMappingByImages', 621
  `AlgebraWithOneHomomorphismByImages', 621
  `AlgebraWithOneHomomorphismByImagesNC', 621
  `AllBlocks', 403
  `AllIrreducibleSolvableGroups', 523
  `All<Library>Groups', 511
  `AllPrimitiveGroups', 511
  `AllSmallGroups', 514
  `AllTransitiveGroups', 511
  `Alpha', 815
  `AlternatingGroup', 505
  `and', 168
    \sub for filters, 117, 169
  An Example of Advanced Dixon-Schneider Calculations, \indexit{746}
  `ANFAutomorphism', 588
  `AntiSymmetricParts', 780
  antisymmetric relation, 312
  `Append', 176
  `AppendTo', 95
    \sub for streams, 101
  Apple, 831, 832
  `ApplicableMethod', 77
  ApplicableMethod, \indexit{77}
  `ApplicableMethodTypes', 77
  `Apply', 197
  `ApplySimpleReflection', 640
  `ApproximateSuborbitsStabilizerPermGroup', 420
  `ARCH_IS_MAC', 34
  `ARCH_IS_UNIX', 34
  `ARCH_IS_WINDOWS', 34
  `arg', special function argument, 46, 56
  Arithmetic for External Representations of Polynomials, \indexit{681}
  Arithmetic for Lists, \indexit{181}
  Arithmetic Operations for Class Functions, \indexit{762}
  Arithmetic Operations for Elements, \indexit{293}
  Arithmetic Operations for General Mappings, \indexit{306}
  Arithmetic Operators, \indexit{48}
  `Arrangements', 147
  arrow notation for functions, 57
  `AsAlgebra', 615
  `AsAlgebraWithOne', 616
  `AsBinaryRelationOnPoints', 313
  `AsBlockMatrix', 236
  `AscendingChain', 367
  `AsDivisionRing', 572
  `AsDuplicateFreeList', 196
  `AsField', 572
  `AsFreeLeftModule', 569
  `AsGroup', 346
  `AsGroupGeneralMappingByImages', 382
  `AsLeftIdeal', 559
  `AsLeftModule', 567
  `AsList', 268
  `AsMagma', 317
  `AsMonoid', 539
  `AsPolynomial', 664
  `AsRightIdeal', 559
  `AsRing', 556
  `AsSemigroup', 532
  `Assert', 80
  `AssertionLevel', 80
  Assertions, \indexit{80}
  `AsSet', 268
  `AssignGeneratorVariables', 329
  assignment, to a list, 174
    \sub to a record, 259
    \sub variable, 50
  Assignments, \indexit{50}
  `AssignNiceMonomorphismAutomorphismGroup', 388
  `AssociatedPartition', 152
  `AssociatedReesMatrixSemigroupOfDClass', 538
  `Associates', 562
  associativity, 48
  `AssocWordByLetterRep', 334
  `AsSortedList', 268
  `AsSSortedList', 268
  `As<Struct>', 285
  `AsSubalgebra', 616
  `AsSubalgebraWithOne', 616
  `AsSubgroup', 347
  `AsSubgroupOfWholeGroupByQuotient', 471
  `AsSubmagma', 318
  `AsSubmonoid', 539
  `AsSubsemigroup', 532
  `AsSubspace', 591
  `AsSub<struct>', 288
  `AsTransformation', 549
  `AsTransformationNC', 549
  `AsTwoSidedIdeal', 559
  `AsVectorSpace', 590
  at exit functions, 73
  ATLAS Irrationalities, \indexit{159}
  `AtlasIrrationality', 161
  atomic irrationalities, 159
  Attributes, \indexit{121}
  Attributes and Operations for Algebras, \indexit{614}
  Attributes and Properties for (Near-)Additive Magmas, \indexit{553}
  Attributes and Properties for Collections, \indexit{269}
  Attributes and Properties for Magmas, \indexit{319}
  Attributes and Properties for Matrix Groups, \indexit{425}
  Attributes and Properties of Character Tables, \indexit{725}
  Attributes and Properties of Elements, \indexit{289}
  Attributes of and Operations on Equivalence Relations, \indexit{314}
  Attributes of Tables of Marks, \indexit{700}
  `AttributeValueNotSet', 122
  `AugmentationIdeal', 655
  `AugmentedCosetTableInWholeGroup', 466
  `AugmentedCosetTableMtc', 466
  `AugmentedCosetTableRrs', 466
  Augmented Coset Tables and Rewriting, \indexit{466}
  automatic loading of gap packages, 836
  `AutomorphismDomain', 387
  `AutomorphismGroup', 387
    \sub for groups with pcgs, 446
  automorphism group, of number fields, 588
  Automorphisms and Equivalence of Character Tables, \indexit{754}
  `AutomorphismsOfTable', 728
\letter B
  $b_N$, 159
  backslash character, 248
  backspace character, 248
  `Backtrace', GAP3 name for `Where', 70
  Backtrack, \indexit{422}
  `BANNER', 841
  `BaseFixedSpace', 227
  `BaseIntersectionIntMats', 237
  `BaseIntMat', 237
  `BaseMat', 230
  `BaseMatDestructive', 230
  `BaseOfGroup', 419
  `BaseOrthogonalSpaceMat', 230
  Bases of Vector Spaces, \indexit{592}
  `BaseStabChain', 419
  `BaseSteinitzVectors', 230
  Basic Actions, \indexit{393}
  Basic Groups, \indexit{504}
  Basic Operations for Class Functions, \indexit{760}
  Basic Operations for Lists, \indexit{172}
  `BasicWreathProductOrdering', 281
  `Basis', 593
  `BasisNC', 593
  `BasisVectors', 594
  `Bell', 146
  `Bernoulli', 146
  `BestQuoInt', 129
  `BestSplittingMatrix', 745
  `BiAlgebraModule', 624
  `BiAlgebraModuleByGenerators', 624
  `BilinearFormMat', 639
  binary relation, 311
  `BinaryRelationByElements', 311
  `BinaryRelationOnPoints', 313
  `BinaryRelationOnPointsNC', 313
  Binary Relations on Points, \indexit{313}
  `BinaryRelationTransformation', 550
  `BindGlobal', 45
  `Binomial', 145
  blank, 41
  `BlistList', 207
  Block Matrices, \indexit{236}
  `BlockMatrix', 236
  `Blocks', 403
  `BlocksInfo', 733
  Block Systems, \indexit{403}
  `BlownUpMat', 232
  `BlownUpVector', 232
  `BlowUpIsomorphism', 426
  BNF, 59
  body, 55
  `BombieriNorm', 670
  Boolean Lists Representing Subsets, \indexit{207}
  bound, 43
  Brauer character, 767
  `BrauerCharacterValue', 790
  `BrauerTable', 719
  `BrauerTableOp', 719
  `BravaisGroup', 429
  `BravaisSubgroups', 429
  `BravaisSupergroups', 429
  Break, \indexit{55}
  break loop message, 69
  Break Loops, \indexit{67}
  `break' statement, 55
  browsing backwards, 22
  browsing backwards one chapter, 23
  browsing forward, 22
  browsing forward one chapter, 23
  browsing the next section browsed, 23
  browsing the previous section browsed, 23
  Browsing through the Sections, \indexit{22}
  bug reports, see If Things Go Wrong, 828
  Building new orderings, \indexit{277}
\letter C
  $c_N$, 159
  Calculating with Group Automorphisms, \indexit{388}
  Calendar Arithmetic, \indexit{255}
  `CallFuncList', 62
  Calling a function with a list argument that is interpreted as several arguments, \indexit{62}
  Cancellation Tests for Rational Functions, \indexit{682}
  `CanComputeIndex', 379
  `CanComputeIsSubset', 379
  `CanComputeSize', 379
  `CanComputeSizeAnySubgroup', 379
  candidates, for permutation characters, 783, 786
  `CanEasilyCompareElements', 292
  `CanEasilyCompareElementsFamily', 292
  `CanEasilyComputePcgs', 432
  `CanEasilySortElements', 292
  `CanEasilySortElementsFamily', 292
  `CanEasilyTestMembership', 379
  `CanonicalBasis', 593
  canonical basis, for matrix spaces, 600
    \sub for row spaces, 600
  `CanonicalGenerators', 639
  `CanonicalPcElement', 434
  `CanonicalPcgs', 437
  `CanonicalPcgsByGeneratorsWithImages', 439
  `Canonical\-Representative\-Determinator\-Of\-External\-Set', 406
  `CanonicalRepresentativeOfExternalSet', 406
  `CanonicalRightCosetElement', 353
  Carmichael's lambda function, 137
  carriage return character, 248
  `CartanMatrix', 638
  `CartanSubalgebra', 635
  `Cartesian', 198
  Categories, \indexit{118}
  Categories and Properties of Algebras, \indexit{613}
  Categories for Streams and the StreamsFamily, \indexit{97}
  Categories of Associative Words, \indexit{327}
  Categories of Matrices, \indexit{219}
  `CategoriesOfObject', 120
  Categories of Words and Nonassociative Words, \indexit{322}
  `CategoryCollections', 265
  `Center', 320
  center, 319
  `CentralCharacter', 770
  central character, 770
  `CentralIdempotentsOfAlgebra', 618
  centraliser, 319
  `Centralizer', 319
    \sub for groups with pcgs, 446
  `CentralizerInGLnZ', 429
  `CentralizerModulo', 368
  `CentralizerSizeLimitConsiderFunction', 447
  `CentralNormalSeriesByPcgs', 441
  `Centre', 320
    \sub for groups with pcgs, 446
  centre, of a character, 769
  `CentreOfCharacter', 769
  `CF', 583
  `ChangeStabChain', 421
  Changing Presentations, \indexit{484}
  Changing the Help Viewer, \indexit{23}
  Changing the Representation, \indexit{286}
  Changing the Structure, \indexit{285}
  `CHAR_INT', 254
  `CHAR_SINT', 254
  `Character', 765
  Character Conversion, \indexit{253}
  `CharacterDegrees', 725
  Character Degrees and Derived Length, \indexit{815}
  `Characteristic', 289
  characteristic, for class functions, 764
  `CharacteristicPolynomial', 231
  characteristic polynomial, for field elements, 574
  `CharacterNames', 729
  characters, 758
    \sub permutation, 783, 786
    \sub symmetrizations of, 779
  `CharacterTable', 719
  Character Table Categories, \indexit{721}
  `CharacterTableDirectProduct', 748
  `CharacterTableFactorGroup', 749
  `CharacterTableIsoclinic', 750
  character tables, 718
    \sub access to, 718
    \sub calculate, 718
    \sub infix operators, 725
    \sub of groups, 718
  `CharacterTableString', 741
  `CharacterTableWithSortedCharacters', 751
  `CharacterTableWithSortedClasses', 752
  `CharacterTableWreathSymmetric', 750
  character value, of group element using powering operator, 763
  `CharsFamily', 250
  `CheapFactorsInt', 134
  `CheckFixedPoints', 804
  `CheckForHandlingByNiceBasis', 605
  `CheckPermChar', 811
  `ChevalleyBasis', 637
  `ChiefNormalSeriesByPcgs', 442
  `ChiefSeries', 365
  `ChiefSeriesThrough', 365
  `ChiefSeriesUnderAction', 365
  `ChineseRem', 130
  Chinese remainder, 131
  `Chomp', 253
  `CIUnivPols', 662
  `ClassElementLattice', 370
  classes, real, 730
  `ClassesSolvableGroup', 446
  `ClassFunction', 765
  class function, 758
  class function objects, 758
  class functions, 801
    \sub as ring elements, 762
  `ClassFunctionSameType', 766
  Class Fusions between Character Tables, \indexit{796}
  Classical Groups, \indexit{506}
  `ClassMultiplicationCoefficient', for character tables, 737
  class multiplication coefficient, 737, 738
  `ClassNames', 729
  `ClassNamesTom', 701
  `ClassOrbit', 730
  `ClassPermutation', 752
  `ClassPositionsOfAgemo', 731
  `ClassPositionsOfCentre', for characters, 769
    \sub for character tables, 731
  `ClassPositionsOfDerivedSubgroup', 731
  `Class\-Positions\-Of\-Direct\-Product\-Decompositions', 731
  `ClassPositionsOfElementaryAbelianSeries', 731
  `ClassPositionsOfFittingSubgroup', 731
  `ClassPositionsOfKernel', 769
  `ClassPositionsOfLowerCentralSeries', 731
  `ClassPositionsOfMaximalNormalSubgroups', 731
  `ClassPositionsOfMinimalNormalSubgroups', 731
  `ClassPositionsOfNormalClosure', 732
  `ClassPositionsOfNormalSubgroup', 756
  `ClassPositionsOfNormalSubgroups', 731
  `ClassPositionsOfSupersolvableResiduum', 732
  `ClassPositionsOfUpperCentralSeries', 731
  `ClassRoots', 730
  `ClassStructureCharTable', 738
  `ClassTypesTom', 700
  `CleanedTailPcElement', 435
  `ClearCacheStats', 83
  `ClearProfile', 82
  clone, an object, 114
  `CloseMutableBasis', 598
  `CloseStream', 98
  `ClosureGroup', 349
  `ClosureGroupAddElm', 349
  `ClosureGroupCompare', 349
  `ClosureGroupDefault', 349
  `ClosureGroupIntest', 349
  `ClosureLeftModule', 568
  `ClosureNearAdditiveGroup', 554
  Closure Operations and Other Constructors, \indexit{313}
  `ClosureRing', 556
  Closures of (Sub)groups, \indexit{349}
  `Closure<Struct>', 285
  `ClosureSubgroup', 349
  `ClosureSubgroupNC', 349
  `Coboundaries', 648
  `Cochain', 647
  `CochainSpace', 647
  `Cocycles', 648
  cocycles, 375
  `CodePcGroup', 457
  `CodePcgs', 457
  Coding a Pc Presentation, \indexit{457}
  coefficient, binomial, 145
  Coefficient List Arithmetic, \indexit{214}
  `Coefficients', 594
  coefficients, for cyclotomics, 157
  `CoefficientsAndMagmaElements', 656
  `CoefficientsFamily', 678
  `CoefficientsMultiadic', 130
  `CoefficientsOfLaurentPolynomial', 670
  `CoefficientsOfUnivariatePolynomial', 664
  `Coefficients\-Of\-Univariate\-Rational\-Function', 664
  `CoefficientsQadic', 130
  `CoefficientsRing', 672
  `CoeffsCyc', 157
  `CoeffsMod', 215
  cohomology, 375
  `COHORTS_PRIMITIVE_GROUPS', 521
  `CoKernelOfAdditiveGeneralMapping', 308
  `CoKernelOfMultiplicativeGeneralMapping', 307
  `CollapsedMat', 807
  `Collected', 196
  Collection Families, \indexit{264}
  `CollectionsFamily', 264
  Coloring the Prompt and Input, \indexit{38}
  `ColorPrompt', 38
  `ColumnIndexOfReesMatrixSemigroupElement', 538
  `Column\-Index\-Of\-Rees\-Zero\-Matrix\-Semigroup\-Element', 538
  `Combinations', 147
  Combinations, Arrangements and Tuples, \indexit{147}
  `CombinatorialCollector', 451
  Combinatorial Numbers, \indexit{145}
  `Comm', 293
    \sub for words, 331
  Command Line Options, \indexit{27}
  comments, 41
  `CommutativeDiagram', 804
  `CommutatorFactorGroup', 368
  `CommutatorLength', 359
    \sub for character tables, 727
  `CommutatorSubgroup', 358
  `Compacted', 195
  `CompanionMat', 232
  `CompareVersionNumbers', 839
  comparison, fp semigroup elements, 544
    \sub operation, 292
    \sub rational functions, 662
  Comparison of Associative Words, \indexit{330}
  Comparison of Class Functions, \indexit{761}
  Comparison of Elements of Finitely Presented Groups, \indexit{460}
  Comparison of Elements of Finitely Presented Semigroups, \indexit{544}
  Comparison of Permutations, \indexit{408}
  Comparison of Rational Functions, \indexit{662}
  Comparison of Words, \indexit{324}
  Comparison Operations for Elements, \indexit{292}
  Comparisons, \indexit{47}
  comparisons, of booleans, 167
    \sub of lists, 180
  Comparisons of Booleans, \indexit{167}
  Comparisons of Cyclotomics, \indexit{159}
  Comparisons of Lists, \indexit{180}
  Comparisons of Records, \indexit{261}
  Comparisons of Strings, \indexit{250}
  `CompatibleConjugacyClasses', 723
  `CompatiblePairs', 455
  Compilation, \indexit{823}
  Compiling Library Code, \indexit{36}
  `Complementclasses', 358
  `ComplementclassesEA', 377
  `ComplementIntMat', 238
  `ComplementSystem', 361
  Completion Files, \indexit{34}
  `ComplexConjugate', 162
    \sub for class functions, 764
  `ComplexificationQuat', 610
  Components of a Dixon Record, \indexit{746}
  `CompositionMapping', 301
    \sub for Frobenius automorphisms, 581
  `CompositionMapping2', 301
  `CompositionMaps', 801
  `CompositionOfStraightLinePrograms', 338
  `CompositionSeries', 365
    \sub for groups with pcgs, 446
  `ComputedBrauerTables', 719
  `ComputedClassFusions', 797
  `ComputedIndicators', 737
  `ComputedIsPSolvableCharacterTables', 736
  `ComputedPowerMaps', 793
  `ComputedPrimeBlockss', 732
  Computing a Pcgs, \indexit{432}
  Computing a Permutation Representation, \indexit{412}
  Computing Pc Groups, \indexit{452}
  Computing Possible Permutation Characters, \indexit{786}
  Computing the Irreducible Characters of a Group, \indexit{741}
  `Concatenation', 195
  concatenation, of lists, 195
  `Conductor', 157
  `ConfluentRws', 341
  `Congruences', for character tables, 809
  Congruences for semigroups, \indexit{535}
  `ConjugacyClass', 355
  Conjugacy Classes, \indexit{355}
  `ConjugacyClasses', attribute, 355
    \sub for character tables, 722
    \sub for groups with pcgs, 446
    \sub for linear groups, 510
  `ConjugacyClassesByOrbits', 356
  `ConjugacyClassesByRandomSearch', 356
  Conjugacy Classes in Classical Groups, \indexit{510}
  Conjugacy Classes in Solvable Groups, \indexit{446}
  `ConjugacyClassesMaximalSubgroups', 369
  `ConjugacyClassesPerfectSubgroups', 372
  `ConjugacyClassesSubgroups', 369
  `ConjugacyClassSubgroups', 369
  conjugate, matrix, 221
    \sub of a word, 331
  `ConjugateDominantWeight', 640
  `ConjugateDominantWeightWithWord', 640
  `ConjugateGroup', 346
  `Conjugates', 575
  `ConjugateSubgroup', 348
  `ConjugateSubgroups', 348
  conjugation, 393
  `ConjugatorAutomorphism', 386
  `ConjugatorAutomorphismNC', 386
  `ConjugatorIsomorphism', 385
  `ConjugatorOfConjugatorIsomorphism', 386
  `ConnectGroupAndCharacterTable', 723
  `ConsiderKernels', 809
  `ConsiderSmallerPowerMaps', 810
  `ConsiderStructureConstants', 801
  `ConsiderTableAutomorphisms', 812
  `ConstantTimeAccessList', 191
  constituent, of a group character, 768
  `ConstituentsCompositionMapping', 302
  `ConstituentsOfCharacter', 769
  Constructing Algebras as Free Algebras, \indexit{607}
  Constructing Algebras by Generators, \indexit{606}
  Constructing Algebras by Structure Constants, \indexit{608}
  Constructing Character Tables from Others, \indexit{748}
  Constructing Domains, \indexit{284}
  Constructing Lie algebras, \indexit{632}
  Constructing Pc Groups, \indexit{450}
  Constructing Subdomains, \indexit{288}
  Constructing Tables of Marks, \indexit{695}
  Constructing Vector Spaces, \indexit{590}
  Construction of Abelian Number Fields, \indexit{583}
  Construction of Stabilizer Chains, \indexit{417}
  Constructors for Basic Groups, \indexit{510}
  `ContainedCharacters', 808
  `ContainedDecomposables', 808
  `ContainedMaps', 803
  `ContainedPossibleCharacters', 806, 807
  `ContainedPossibleVirtualCharacters', 806, 807
  `ContainedSpecialVectors', 806, 807
  `ContainedTom', 705
  `ContainingTom', 705
  `ContinuedFractionApproximationOfRoot', 141
  `ContinuedFractionExpansionOfRoot', 141
  Continued Fractions, \indexit{141}
  `continue' statement, 55
  Conventions for Character Tables, \indexit{722}
  convert, to a string, 249
  Converting Groups to Finitely Presented Groups, \indexit{468}
  `ConvertToCharacterTable', 720
  `ConvertToCharacterTableNC', 720
  `ConvertToMatrixRep', 233
  `ConvertToMatrixRepNC', 233
  `ConvertToRangeRep', 205
  `ConvertToStringRep', 249
  `ConvertToTableOfMarks', 699
  `ConvertToVectorRep', 213
  `ConvertToVectorRepNC', 213
  `ConwayPolynomial', 581
  Conway Polynomials, \indexit{581}
  coprime, 48
  copy, 114
    \sub an object, 114
  `COPY_LIST_ENTRIES', 176
  `CopyOptionsDefaults', 421
  Copyrights, \indexit{835}
  `CopyStabChain', 421
  `Core', 357
  `CorrespondingGeneratorsByModuloPcgs', 439
  coset, 352
  `CosetLeadersMatFFE', 216
  Cosets, \indexit{352}
  `CosetTable', 462
  `CosetTableBySubgroup', 463
  `CosetTableDefaultLimit', 464
  `CosetTableDefaultMaxLimit', 464
  `CosetTableFromGensAndRels', 463
  `CosetTableInWholeGroup', 466
  `CosetTableOfFpSemigroup', 547
  Coset Tables and Coset Enumeration, \indexit{462}
  Coset tables for subgroups in the whole group, \indexit{466}
  `CosetTableStandard', 465
  CRC, 36
  `CrcFile', 95
    \sub example, 36
  CRC Numbers, \indexit{36}
  `CreateCompletionFiles', 34
  `CreateCompletionFilesPkg', 840
  Creating Character Tables, \indexit{718}
  Creating Class Functions from Values Lists, \indexit{765}
  Creating Class Functions using Groups, \indexit{766}
  Creating Finite Fields, \indexit{580}
  Creating Finitely Presented Groups, \indexit{459}
  Creating Finitely Presented Semigroups, \indexit{543}
  Creating Group Homomorphisms, \indexit{380}
  Creating Groups, \indexit{345}
  Creating Mappings, \indexit{301}
  Creating Permutations, \indexit{410}
  Creating Presentations, \indexit{476}
  Creation of Algebraic Extensions, \indexit{683}
  Creation of Rational Functions, \indexit{680}
  Credit, \indexit{21}
  `CrystGroupDefaultAction', 430
  `Cycle', 401
  `CycleLength', 401
  `CycleLengths', 401
  `Cycles', 401
  `CycleStructureClass', 770
  `CycleStructurePerm', 409
  `CyclicExtensionsTom', 705
  `CyclicGroup', 504
  `CyclotomicField', 583
  cyclotomic field elements, 155
  cyclotomic fields, canonicalbasis, 586
  `CyclotomicPolynomial', 668
  Cyclotomic Polynomials, \indexit{668}
  `Cyclotomics', 155
  cyclotomics, defaultfield, 584
\letter D
  $d_N$, 159
  Darstellungsgruppe, see `EpimorphismSchurCover', 378
  `DataType', 125
  data type, unknown, 165
  `DayDMY', 256
  `DaysInMonth', 255
  `DaysInYear', 255
  Debugging Recursion, \indexit{84}
  DEC, 241
  `DeclareAutoPackage', 840
  `DeclareHandlingByNiceBasis', 604
  `DeclareInfoClass', 79
  `DeclarePackage', 840
  `DeclarePackageAutoDocumentation', 840
  `DeclarePackageDocumentation', 840
  `DecodeTree', 494
  DecodeTree, \indexit{494}
  decompose, a group character, 768
  `DecomposedFixedPointVector', 705
  `DecomposeTensorProduct', 649
  `Decomposition', 241
  `DecompositionInt', 242
  `DecompositionMatrix', 734
  decomposition matrix, 241
  Decompositions, \indexit{241}
  `Decreased', 777
  `DefaultField', 572
    \sub for cyclotomics, 158
    \sub for finite field elements, 580
  `DefaultFieldByGenerators', 572
  `DefaultFieldOfMatrix', 222
  `DefaultFieldOfMatrixGroup', 425
  `DefaultRing', 555
    \sub for finite field elements, 580
  `DefaultRingByGenerators', 556
  `DefaultStabChainOptions', 418
  Defining a Pcgs Yourself, \indexit{432}
  `DefiningPolynomial', 573
  `DefiningQuotientHomomorphism', 472
  `DegreeFFE', 578
  `DegreeIndeterminate', 666
  `DegreeOfBinaryRelation', 312
  `DegreeOfCharacter', 768
  `DegreeOfLaurentPolynomial', 665
  `DegreeOfTransformation', 548
  `DegreeOfTransformationSemigroup', 534
  `DegreeOverPrimeField', 573
  `Delta', 815
  denominator, of a rational, 144
  `DenominatorCyc', 158
  `DenominatorOfModuloPcgs', 438
  `DenominatorOfRationalFunction', 664
  `DenominatorRat', 144
  deprecated, 840
  `DepthOfPcElement', 434
  `DepthOfUpperTriangularMatrix', 231
  `Derangements', 149
  `Derivations', 633
  `Derivative', 667
  `DerivedLength', 366
  `DerivedSeriesOfGroup', 366
  `DerivedSubgroup', 358
  `DerivedSubgroupsTom', 704
  `DerivedSubgroupsTomPossible', 704
  `DerivedSubgroupsTomUnique', 704
  `DerivedSubgroupTom', 704
  `DescriptionOfRootOfUnity', 158
  `Determinant', 223
  determinant character, 770
  `DeterminantIntMat', 241
  `DeterminantMat', 223
  `DeterminantMatDestructive', 223
  `DeterminantMatDivFree', 223
  Determinant of an integer matrix, \indexit{241}
  `DeterminantOfCharacter', 770
  Developing rewriting systems, \indexit{343}
  `DiagonalizeIntMat', 239
  `DiagonalizeMat', 228
  `DiagonalMat', 224
  `DiagonalOfMat', 231
  `Difference', 272
  `DifferenceBlist', 208
  `DihedralGroup', 505
  `Dimension', 569
  `DimensionOfHighestWeightModule', 649
  `DimensionOfMatrixGroup', 425
  `DimensionOfVectors', 599
  `DimensionsLoewyFactors', 367
  `DimensionsMat', 222
  Directories, \indexit{91}
  `DirectoriesLibrary', 91
  `DirectoriesPackageLibrary', 838
  `DirectoriesPackagePrograms', 839
  `DirectoriesSystemPrograms', 92
  `Directory', 91
  `DirectoryContents', 92
  `DirectoryCurrent', 91
  `DirectoryTemporary', 91
  `DirectProduct', 499
  `DirectProductOp', 499
  Direct Products, \indexit{499}
  `DirectSumDecomposition', 618
    \sub for Lie algebras, 637
  Direct Sum Decompositions, \indexit{637}
  `DirectSumOfAlgebraModules', 629
    \sub for Lie algebras, 652
  `DirectSumOfAlgebras', 617
  `DisableAttributeValueStoring', 123
  disable automatic loading, 836
  `Discriminant', 667
  `Display', 66
    \sub for character tables, 738, 765
    \sub for tables of marks, 697
  `DisplayCacheStats', 83
  `DisplayCompositionSeries', 365
  `DisplayEggBoxOfDClass', 536
  `DisplayImfInvariants', 525
  `DisplayInformationPerfectGroups', 518
  `DisplayOptions', 740
  `DisplayOptionsStack', 89
  `DisplayProfile', 82
  `DisplayRevision', 84
  `DistancesDistributionMatFFEVecFFE', 216
  `DistancesDistributionVecFFEsVecFFE', 216
  `DistanceVecFFE', 216
  Distinguished Subalgebras, \indexit{634}
  division, 48
    \sub operation, 293
  `DivisionRingByGenerators', 572
  division rings, 571
  divisors, of an integer, 134
  `DivisorsInt', 134
  Dixon-Schneider algorithm, 744
  `DixonInit', 745
  `DixonRecord', 745
  `DixonSplit', 745
  `DixontinI', 745
  `DMYDay', 256
  `DMYhmsSeconds', 257
  `DnLattice', 778
  `DnLatticeIterative', 779
  `do', 53
  document formats (text, dvi, ps, pdf, html), 23
  `Domain', 289
  `DomainByGenerators', 289
  Domain Categories, \indexit{286}
  Domains, \indexit{111}
  Domains Generated by Class Functions, \indexit{791}
  Domains of Subspaces of Vector Spaces, \indexit{592}
  `DominantCharacter', 648
  `DominantWeights', 648
  `DoubleCoset', 354
  `DoubleCosetRepsAndSizes', 355
  Double Cosets, \indexit{354}
  `DoubleCosets', operation, 354
  `DoubleCosetsNC', operation, 354
  doublequote character, 248
  doublequotes, 246
  `DownEnv', 71
  Dummy Streams, \indexit{106}
  duplicate free, 191
  `DuplicateFreeList', 196
  Duplication of Lists, \indexit{178}
  Duplication of Objects, \indexit{114}
  `DxIncludeIrreducibles', 745
\letter E
  `E', 155
  $e_N$, 159
  `EANormalSeriesByPcgs', 440
  `Earns', 402
  `EB', 159
  `EC', 159
  Echelonized Matrices, \indexit{228}
  `ED', 159
  `Edit', 74
  Editing Files, \indexit{74}
  Editor Support, \indexit{75}
  `EE', 159
  `EF', 159
  Efficiency of Homomorphisms, \indexit{383}
  `EG', 159
  `EggBoxOfDClass', 536
  `EH', 159
  `EI', 160
  `Eigenspaces', 227
  `Eigenvalues', 227
  `EigenvaluesChar', 771
  `Eigenvectors', 227
  Eigenvectors and eigenvalues, \indexit{227}
  `EJ', 160
  `EK', 160
  `EL', 160
  `ElementaryAbelianGroup', 505
  `ElementaryAbelianSeries', 366
  `ElementaryAbelianSeriesLargeSteps', 366
  Elementary Divisors, \indexit{228}
  `ElementaryDivisorsMat', 228
  `ElementaryDivisorsMatDestructive', 228
  Elementary Operations for a Pcgs, \indexit{433}
  Elementary Operations for a Pcgs and an Element, \indexit{434}
  Elementary Operations for Integers, \indexit{127}
  Elementary Operations for Rationals, \indexit{143}
  Elementary Tietze Transformations, \indexit{487}
  `ElementOfFpGroup', 461
  `ElementOfFpSemigroup', 545
  `ElementOfMagmaRing', 656
  `ElementOrdersPowerMap', 794
  `ElementProperty', 422
  `Elements', 269
  elements, definition, 110
    \sub of a list or collection, 269
  Elements as equivalence classes, \indexit{110}
  `ElementsFamily', 264
  Elements in Algebraic Extensions, \indexit{683}
  Elements of Free Magma Rings, \indexit{656}
  Elements of pc groups, \indexit{449}
  `ElementsStabChain', 420
  Elements with Prescribed Images, \indexit{398}
  element test, for lists, 180
  `elif', 51
  `EliminatedWord', 332
  `EliminationOrdering', 676
  `else', 51
  `EM', 160
  `emacs', 75
  `Embedding', 302
    \sub example for direct products, 499
    \sub example for semidirect products, 501
    \sub example for wreath products, 502
    \sub for group products, 503
    \sub for Lie algebras, 632
    \sub for magma rings, 656
  embeddings, find all, 389
  Embeddings and Projections for Group Products, \indexit{503}
  `EmptyBinaryRelation', 311
  `EmptyMatrix', 224
  `EmptySCTable', 608
  `EmptyStabChain', 421
  `EnableAttributeValueStoring', 123
  `End', 602
  `end', 55
  Enlarging Internally Represented Lists, \indexit{180}
  `Enumerator', 265
  `EnumeratorByBasis', 595
  `EnumeratorByFunctions', 266
  Enumerators, \indexit{205}
  `EnumeratorSorted', 265
  environment, 55
  `EpimorphismFromFreeGroup', 349
  `EpimorphismNilpotentQuotient', 473
  `EpimorphismPGroup', 473
  `EpimorphismQuotientSystem', 472
  epimorphisms, find all, 389
  `EpimorphismSchurCover', 378
  equality, associative words, 330
    \sub elements of finitely presented groups, 460
    \sub nonassociative words, 324
    \sub of records, 261
    \sub operation, 292
    \sub pcwords, 449
  Equality and Comparison of Domains, \indexit{284}
  equality test, 47
    \sub for permutations, 408
  equivalence class, 315
  Equivalence Classes, \indexit{315}
  `EquivalenceClasses', attribute, 315
  `EquivalenceClassOfElement', 315
  `EquivalenceClassOfElementNC', 315
  `EquivalenceClassRelation', 315
  equivalence relation, 312, 314
  `EquivalenceRelationByPairs', 314
  `EquivalenceRelationByPairsNC', 314
  `EquivalenceRelationByPartition', 314
  `EquivalenceRelationByPartitionNC', 314
  `EquivalenceRelationByProperty', 314
  `EquivalenceRelationByRelation', 314
  `EquivalenceRelationPartition', 314
  Equivalence Relations, \indexit{314}
  `ER', 160
  `Error', 72
  Error, \indexit{72}
  `ErrorCount', 72
  ErrorCount, \indexit{72}
  `ErrorNoTraceBack', 68
  errors, syntax, 64
  `ES', 160
  escaped characters, 248
  escaping non-special characters, 248
  `ET', 160
  `EU', 160
  `EuclideanDegree', 563
  `EuclideanQuotient', 563
  `EuclideanRemainder', 564
  Euclidean Rings, \indexit{563}
  Euler's totient function, 136
  `EulerianFunction', 364
  `EulerianFunctionByTom', 706
  `EV', 160
  `EvalStraightLineProgElm', 339
  `EvalString', 255
  evaluation, 42
    \sub strings, 254
  `EW', 160
  `EX', 160
  `ExactSizeConsiderFunction', 374
  `Exec', 109
  Exec, \indexit{109}
  execution, 49
  exit, 73
  expanded form of monomials, 679
  Expert Windows installation, \indexit{834}
  `Exponent', 364
    \sub for character tables, 727
  exponent, of the prime residue group, 137
  exponentiation, operation, 293
  `ExponentOfPcElement', 434
  `ExponentsConjugateLayer', 435
  `ExponentsOfCommutator', 435
  `ExponentsOfConjugate', 435
  `ExponentsOfPcElement', 434
  `ExponentsOfRelativePower', 435
  Exponents of Special Products, \indexit{435}
  `ExponentSumWord', 331
  `ExponentSyllable', 333
  Expressing Group Elements as Words in Generators, \indexit{349}
  Expressions, \indexit{42}
  `ExtendedPcgs', 437
  `ExtendStabChain', 421
  `Extension', 454
  `ExtensionNC', 454
  `ExtensionRepresentatives', 455
  `Extensions', 454
  Extensions of the p-adic Numbers, \indexit{686}
  `ExteriorPowerOfAlgebraModule', 652
  `ExternalOrbit', 405
  `ExternalOrbits', 405
  `ExternalOrbitsStabilizers', 405
  External Representation for Nonassociative Words, \indexit{326}
  external representation of polynomials, 679
  `ExternalSet', 404
  External Sets, \indexit{404}
  `ExternalSubset', 405
  `Extract', 775
  `ExtraspecialGroup', 505
  `ExtRepDenominatorRatFun', 680
  `ExtRepNumeratorRatFun', 680
  `ExtRepOfObj', external representation, for cyclotomics, 158
  `ExtRepPolynomialRatFun', 680
  `EY', 160
\letter F
  $f_N$, 159
  `FactorCosetAction', 400
    \sub for fp groups, 463
  `FactorCosetOperation', 463
  `FactorFreeSemigroupByRelations', 543
  `FactorGroup', 368
  `FactorGroupFpGroupByRels', 459
  `FactorGroupNC', 368
  `FactorGroupNormalSubgroupClasses', 756
  Factor Groups, \indexit{368}
  Factor Groups of Polycyclic Groups - Modulo Pcgs, \indexit{438}
  Factor Groups of Polycyclic Groups in their Own Representation, \indexit{439}
  `FactorGroupTom', 706
  `Factorial', 145
  `Factorization', 350
  factorization, 349
  `Factors', 563
    \sub of univariate polynomial, 668
  `FactorsInt', 132
  `FactorsOfDirectProduct', 749
  `FactorsSquarefree', 669
  Fail, \indexit{167}
  `fail', 167
  `FaithfulModule', 628
    \sub for Lie algebras, 646
  Families, \indexit{116}
  `FamiliesOfGeneralMappingsAndRanges', 310
  `FamiliesOfRows', 755
  `FamilyForOrdering', 278
  `FamilyObj', 116
  `FamilyPcgs', 449
  `FamilyRange', 310
  `FamilySource', 310
  FAQ, 827
  features, under UNIX, 27
  `fi', 51
  `Fibonacci', 153
  Fibonacci and Lucas Sequences, \indexit{153}
  `Field', 571
  `FieldExtension', 573
  field homomorphisms, Frobenius, 581
  `FieldOfMatrixGroup', 425
  `FieldOverItselfByGenerators', 573
  fields, 571
  File Access, \indexit{93}
  `FileDescriptorOfStream', 98
  `Filename', 92
  Filename, \indexit{92}
  File Operations, \indexit{94}
  File Streams, \indexit{103}
  `Filtered', 199
  Filters, \indexit{117}
  Filters Controlling the Arithmetic Behaviour of Lists, \indexit{182}
  Finding Positions in Lists, \indexit{188}
  Finding Submodules, \indexit{689}
  `FindSl2', 644
  Finish Installation and Cleanup, \indexit{825}
  Finite Field Elements, \indexit{577}
  Finitely Presented Lie Algebras, \indexit{644}
  Finitely presented monoids, \indexit{545}
  finiteness test, for a list or collection, 269
  Finite Perfect Groups, \indexit{516}
  `First', 200
  `FittingSubgroup', 359
  `Flat', 196
  flush character, 248
  For, \indexit{53}
  `ForAll', 200
  `ForAny', 200
  `for' loop, 53
  `FpElmComparisonMethod', 460
  `FpGroupPresentation', 477
  `FpGrpMonSmgOfFpGrpMonSmgElement', 543
  `FpLieAlgebraByCartanMatrix', 645
  frame, 780, 781
  `FrattiniSubgroup', 359
    \sub for groups with pcgs, 446
  `FreeAlgebra', 607
  `FreeAlgebraWithOne', 607
  `FreeAssociativeAlgebra', 607
  `FreeAssociativeAlgebraWithOne', 607
  `FreeGeneratorsOfFpGroup', 460
  `FreeGeneratorsOfFpSemigroup', 544
  `FreeGeneratorsOfWholeGroup', 460
  `FreeGroup', 328
  `FreeGroupOfFpGroup', 460
  Free Groups, Monoids and Semigroups, \indexit{328}
  `FreeLeftModule', 569
  `FreeLieAlgebra', 633
  `FreeMagma', 325
  `FreeMagmaRing', 655
  Free Magma Rings, \indexit{655}
  Free Magmas, \indexit{325}
  `FreeMagmaWithOne', 325
  Free Modules, \indexit{569}
  `FreeMonoid', 540
    \sub with example, 328
  `FreeMonoidOfRewritingSystem', 547
  `FreeSemigroup', 328
    \sub with examples, 533
  `FreeSemigroupOfFpSemigroup', 544
  `FreeSemigroupOfRewritingSystem', 547
  Frobenius automorphism, 581
  `FrobeniusAutomorphism', 581
  FrobeniusAutomorphism, \indexit{581}
  `FrobeniusCharacterValue', 790
  `FullMatrixAlgebra', 610
  `FullMatrixAlgebraCentralizer', 618
  `FullMatrixLieAlgebra', 633
  `FullMatrixModule', 570
  `FullMatrixSpace', 599
  `FullRowModule', 570
  `FullRowSpace', 599
  `FullTransformationSemigroup', 534
  Function, \indexit{55}
  `function', 55
  `FunctionAction', 404
  function call, 46
    \sub with arguments, 46
    \sub with options, 47
  Function Calls, \indexit{46}
  `FunctionOperation', 840
  functions, 61, 300
    \sub definition by arrow notation, 57
    \sub definition of, 55
    \sub recursive, 55
    \sub with a variable number of arguments, 46, 56
  `FunctionsFamily', 63
  Functions for Coding Theory, \indexit{216}
  Functions for GAP Packages, \indexit{837}
  Functions that do nothing, \indexit{63}
  Function that Modify Boolean Lists, \indexit{209}
  Function Types, \indexit{63}
  `FusionCharTableTom', 712
  `FusionConjugacyClasses', 797
  `FusionConjugacyClassesOp', 797
  fusions, 796
  `FusionsAllowedByRestrictions', 812
  `FusionsTom', 701
\letter G
  $G$-sets, 392, 404
  $g_N$, 159
  `gac', 35
  Galois Action, \indexit{573}
  Galois Conjugacy of Cyclotomics, \indexit{162}
  `GaloisCyc', 162
    \sub for class functions, 764
  `GaloisField', 580
  `GaloisGroup', of field, 574
    \sub of rational class of a group, 357
  Galois Groups of Abelian Number Fields, \indexit{588}
  `GaloisMat', 163
  `GaloisStabilizer', 585
  `GaloisType', 669
  `gap.rc', 32, 33
  GAP3, 33
  `Gap3CatalogueIdGroup', 514
  GAP for Macintosh OS X, \indexit{831}
  GAP for MacOS, \indexit{832}
  `GAPInfo', 841
  `GAPInfo.RootPaths', 29
  `GapInputPcGroup', 453
  `GapInputSCTable', 608
  `GAPKB_REW', 546
  GAP Root Directory, \indexit{90}
  `GasmanLimits', 87
  `GasmanMessageStatus', 86
  `GasmanStatistics', 86
  Gaussian algorithm, 226
  `GaussianIntegers', 589
  `GaussianRationals', 584
  Gaussians, \indexit{589}
  `Gcd', 564
  Gcd and Lcm, \indexit{564}
  `Gcdex', 130
  `GcdInt', 129
  `GcdOp', 564
  `GcdRepresentation', 564
  `GcdRepresentationOp', 565
  General Binary Relations, \indexit{311}
  `GeneralisedEigenspaces', 227
  `GeneralisedEigenvalues', 227
  generalized characters, 758
  `GeneralizedEigenspaces', 227
  `GeneralizedEigenvalues', 227
  `GeneralLinearGroup', 507
  `GeneralMappingByElements', 301
  General Mappings, \indexit{309}
  `GeneralMappingsFamily', 310
  `GeneralOrthogonalGroup', 508
  `GeneralUnitaryGroup', 507
  Generating Fields, \indexit{571}
  Generating modules, \indexit{567}
  Generating Rings, \indexit{555}
  generator, of the prime residue group, 138
  `GeneratorsOfAdditiveGroup', 553
  `GeneratorsOfAdditiveMagma', 553
  `GeneratorsOfAdditiveMagmaWithZero', 553
  `GeneratorsOfAlgebra', 614
  `GeneratorsOfAlgebraModule', 625
  `GeneratorsOfAlgebraWithOne', 614
  `GeneratorsOfDivisionRing', 572
  `GeneratorsOfDomain', 289
  `Generators\-Of\-Equivalence\-Relation\-Partition', 314
  `GeneratorsOfField', 572
  `GeneratorsOfGroup', 346
  `GeneratorsOfIdeal', 558
  `GeneratorsOfLeftIdeal', 559
  `GeneratorsOfLeftModule', 567
  `GeneratorsOfLeftOperatorAdditiveGroup', 567
  `GeneratorsOfLeftVectorSpace', 591
  `GeneratorsOfMagma', 319
  `GeneratorsOfMagmaWithInverses', 319
  `GeneratorsOfMagmaWithOne', 319
  `GeneratorsOfMonoid', 539
  `GeneratorsOfNearAdditiveGroup', 553
  `GeneratorsOfNearAdditiveMagma', 553
  `GeneratorsOfNearAdditiveMagmaWithZero', 553
  `GeneratorsOfPresentation', 476
  `GeneratorsOfRightIdeal', 559
  `GeneratorsOfRightModule', 568
  `GeneratorsOfRightOperatorAdditiveGroup', 568
  `GeneratorsOfRing', 556
  `GeneratorsOfRingWithOne', 560
  `GeneratorsOfRws', 341
  `GeneratorsOfSemigroup', 533
  `GeneratorsOf<Struct>', 285
  `GeneratorsOfTwoSidedIdeal', 558
  `GeneratorsOfVectorSpace', 591
  `GeneratorsPrimeResidues', 137
  `GeneratorsSmallest', 375
  `GeneratorsSubgroupsTom', 710
  `GeneratorSyllable', 333
  Generic Construction of Tables of Marks, \indexit{714}
  `GetFusionMap', 798
  Get the Archives, \indexit{822}
  getting help, 22
  `GF', 580
  `GL', 507
  GL and SL, \indexit{426}
  Global Memory Information, \indexit{86}
  `GModuleByMats', 688
  `GO', 508
  `GQuotients', 389
  `Grading', 619
  Green's Relations, \indexit{535}
  `GreensDClasses', 537
  `GreensDClassOfElement', 536
  `GreensDRelation', 536
  `GreensHClasses', 537
  `GreensHClassOfElement', 536
  `GreensHRelation', 536
  `GreensJClasses', 537
  `GreensJClassOfElement', 536
  `GreensJRelation', 536
  `GreensLClasses', 537
  `GreensLClassOfElement', 536
  `GreensLRelation', 536
  `GreensRClasses', 537
  `GreensRClassOfElement', 536
  `GreensRRelation', 536
  Groebner Bases, \indexit{677}
  `GroebnerBasis', 677
  `GroebnerBasisNC', 677
  `Group', 345
  group actions, 392, 393
    \sub operations syntax, 392
  Group Actions - Name Changes, \indexit{840}
  group algebra, 654
  Group Automorphisms, \indexit{385}
  `GroupByRws', 451
  `GroupByRwsNC', 451
  group characters, 758
  Group Elements, \indexit{345}
  `GroupGeneralMappingByImages', 381
  `GroupHClassOfGreensDClass', 537
  `GroupHomomorphismByFunction', 381
  `GroupHomomorphismByImages', 380
  `GroupHomomorphismByImagesNC', 380
  `GroupOfPcgs', 433
  group operations, 393, 840
  Group Properties, \indexit{362}
  `GroupRing', 655
  group ring, 654
  Groups of Automorphisms, \indexit{387}
  `GroupStabChain', 420
  `GroupWithGenerators', 346
  `GU', 507
\letter H
  $h_N$, 159
  `HallSubgroup', 360
  `HallSystem', 361
    \sub for groups with pcgs, 446
  Handling of Streams in the Background, \indexit{106}
  `HasAbelianFactorGroup', 368
  `HasElementaryAbelianFactorGroup', 368
  `HasIndeterminateName', 661
  `HasParent', 287
  `HasseDiagramBinaryRelation', 313
  `HeadPcElementByNumber', 435
  `HenselBound', 670
  hermite normal form, 841
  `HermiteNormalFormIntegerMat', 239
  `HermiteNormalFormIntegerMatTransform', 239
  `HeuristicCancelPolynomials', 682
  `HexStringInt', 251
  `HighestWeightModule', 651
  History of Character Theory Stuff in GAP, \indexit{717}
  `HMSMSec', 256
  `Hom', 602
  `HomeEnumerator', 404
  Homomorphism for very large groups, \indexit{384}
  `HomomorphismQuotientSemigroup', 535
  homomorphisms, find all, 389
  homomorphisms, Frobenius, field, 581
  Homomorphisms of Algebras, \indexit{620}
  `HomomorphismTransformationSemigroup', 534
  How to Implement New Kinds of Vector Spaces, \indexit{604}
  `HumanReadableDefinition', 708
\letter I
  $i_N$, 160
  `Ideal', 557
  `IdealByGenerators', 558
  `IdealNC', 558
  Ideals, \indexit{612}
  Ideals in Rings, \indexit{557}
  Ideals of semigroups, \indexit{534}
  `Idempotents', 320
  `IdempotentsTom', 701
  `IdempotentsTomInfo', 701
  Identical Lists, \indexit{177}
  Identical Objects, \indexit{111}
  Identical Records, \indexit{260}
  `IdentificationOfConjugacyClasses', 723
  `Identifier', for character tables, 729
    \sub for tables of marks, 702
  Identifiers, \indexit{42}
  `Identity', 289
  `IdentityBinaryRelation', 311
  `IdentityFromSCTable', 609
  `IdentityMapping', 302
  `IdentityMat', 224
  `IdentityTransformation', 548
  `IdFunc', 63
  `IdGap3SolvableGroup', 514
  `IdGroup', 514
  `IdSmallGroup', 514
  `IdsOfAllSmallGroups', 514
  If, \indexit{51}
  `if' statement, 51
  If Things Go Wrong, \indexit{827}
  `Image', 304
    \sub for Frobenius automorphisms, 581
  image, vector under matrix, 221
  `ImageElm', 304
  `ImageListOfTransformation', 549
  `Images', 304
  `ImagesElm', 303
  `ImageSetOfTransformation', 549
  `ImagesRepresentative', 303
  `ImagesSet', 303
  `ImagesSmallestGenerators', 384
  `ImagesSource', 303
  Images under Mappings, \indexit{303}
  `ImfInvariants', 527
  `ImfMatrixGroup', 528
  `ImfNumberQClasses', 525
  `ImfNumberQQClasses', 525
  `ImfNumberZClasses', 525
  `Immutable', 113
  `ImmutableBasis', 598
  `ImmutableMatrix', 233
  `in', for collections, 273
    \sub for lists, 180
    \sub for strictly sorted lists, 193
    \sub operation for, 273
  `IndependentGeneratorsOfAbelianGroup', 375
  `Indeterminate', 660
  `IndeterminateName', 661
  `Indeterminateness', 806
  `IndeterminateNumberOfLaurentPolynomial', 671
  `Indeterminate\-Number\-Of\-Univariate\-Rational\-Function', 661
  `Indeterminate\-Of\-Univariate\-Rational\-Function', 661
  Indeterminates, \indexit{660}
  `IndeterminatesOfPolynomialRing', 672
  `Index', 347
  `IndexInWholeGroup', 347
  `IndexNC', 347
  Index numbers of primitive groups, \indexit{522}
  `Indicator', 737
  `IndicatorOp', 737
  `IndicesCentralNormalSteps', 440
  `IndicesChiefNormalSteps', 441
  `IndicesEANormalSteps', 440
  `IndicesInvolutaryGenerators', 465
  `IndicesNormalSteps', 442
  `IndicesOfAdjointBasis', 615
  `IndicesPCentralNormalStepsPGroup', 441
  `IndicesStabChain', 420
  `Indirected', 802
  Induced Actions, \indexit{690}
  `InducedAutomorphism', 388
  `InducedClassFunction', 772
  `InducedClassFunctions', 772
  `InducedCyclic', 773
  `InducedPcgs', 436
  `InducedPcgsByGenerators', 436
  `InducedPcgsByGeneratorsNC', 436
  `InducedPcgsByPcSequence', 436
  `InducedPcgsByPcSequenceAndGenerators', 437
  `InducedPcgsByPcSequenceNC', 436
  `InducedPcgsWrtFamilyPcgs', 449
  `InducedPcgsWrtSpecialPcgs', 444
  `Inequalities', 789
  inequality, of records, 261
  inequality test, 47
  `InertiaSubgroup', 770
  Infinity, \indexit{158}
  `infinity', 158
  inflated class functions, 771
  `Info', 79
  `InfoAlgebra', 606
  `InfoAttributes', 123
  `InfoBckt', 422
  `InfoCharacterTable', 722
  `InfoCoh', 377
  `InfoComplement', 358
  `InfoCoset', 355
  `InfoFpGroup', 459
  Info Functions, \indexit{79}
  `InfoGroebner', 678
  `InfoGroup', 346
  `InfoLattice', 372
  `InfoLevel', 79
  `InfoMatrix', 219
  `InfoMonomial', 814
  `InfoNumtheor', 136
  `InfoOptions', 89
  `InfoPcSubgroup', 375
  Information about a function, \indexit{61}
  Information about the version used, \indexit{84}
  `InfoText', 730
  `InfoTom', 699
  `InfoWarning', 80
  `InitFusion', 811
  `InitPowerMap', 809
  `InjectionZeroMagma', 318
  `InnerAutomorphism', 386
  `InnerAutomorphismNC', 386
  `InnerAutomorphismsAutomorphismGroup', 387
  inner product, of group characters, 768
  Input-Output Streams, \indexit{105}
  `InputLogTo', 95
    \sub for streams, 102
    \sub stop logging input, 95
  `InputOutputLocalProcess', 105
  `InputTextFile', 103
  `InputTextNone', 106
  `InputTextString', 104
  `InputTextUser', 104
  `InsertTrivialStabilizer', 421
  `InstallAtExit', 73
  installation, 821
  Installation of GAP for MacOS, \indexit{832}
  Installation Overview, \indexit{821}
  `InstallCharReadHookFunc', 106
  `InstalledPackageVersion', 838
  `InstallFactorMaintenance', 295
  `InstallHandlingByNiceBasis', 604
  Installing a GAP Package, \indexit{836}
  `InstallIsomorphismMaintenance', 295
  `InstallSubsetMaintenance', 295
  `Int', 127
    \sub for cyclotomics, 156
    \sub for strings, 254
  `INT_CHAR', 254
  integer part of a quotient, 129
  `Integers', 126
  Integral Bases of Abelian Number Fields, \indexit{586}
  `IntegralizedMat', 242
  `IntegratedStraightLineProgram', 338
  `IntermediateGroup', 367
  `IntermediateSubgroups', 367
  Internally Represented Cyclotomics, \indexit{164}
  Internally Represented Strings, \indexit{249}
  `InterpolatedPolynomial', 566
  `IntersectBlist', 209
  `Intersection', 271
    \sub for groups with pcgs, 446
  intersection, of collections, 271
    \sub of sets, 194
  `Intersection2', 271
  `IntersectionBlist', 208
  `IntersectionsTom', 706
  `IntersectSet', 194
  `IntFFE', 579
  `IntFFESymm', 579
  `IntHexString', 254
  `IntScalarProducts', 806, 807
  `IntVecFFE', 579
  `InvariantBilinearForm', 427
  `InvariantElementaryAbelianSeries', 366
  Invariant Forms, \indexit{427}, \indexit{691}
  `InvariantLattice', 429
  `InvariantQuadraticForm', 427
  `InvariantSesquilinearForm', 427
  `Invariant\-Subgroups\-Elementary\-Abelian\-Group', 373
  `Inverse', 291
  inverse, group homomorphism, 382
    \sub matrix, 221
    \sub of class function, 763
  `InverseAttr', 291
  `InverseClasses', 730
  `InverseGeneralMapping', 301
  `InverseImmutable', 291
  `InverseMap', 802
  `InverseMatMod', 235
  `InverseMutable', 291
  `InverseOp', 291
  `InverseRepresentative', 420
  `InverseSameMutability', 291
  `InverseSM', 291
  Invoking the Help, \indexit{22}
  `Irr', 725
  irrationalities, 155
  `IrrBaumClausen', 742
  `IrrConlon', 742
  `IrrDixonSchneider', 742
  Irreducibility Tests, \indexit{689}
  irreducible character, 767
  irreducible characters, computation, 745
  `IrreducibleDifferences', 774
  Irreducible Maximal Finite Integral Matrix Groups, \indexit{524}
  `IrreducibleModules', 744
    \sub for groups with pcgs, 446
  `IrreducibleRepresentations', 742
  `IrreducibleRepresentationsDixon', 743
  `IrreducibleSolvableGroup', 523
  `IrreducibleSolvableGroupMS', 523
  Irreducible Solvable Matrix Groups, \indexit{523}
  `Is16BitsFamily', 334
  `Is32BitsFamily', 334
  `Is8BitsFamily', 334
  `IsAbelian', 320
    \sub for character tables, 727
  `IsAbelianNumberField', 585
  `IsAbelianNumberFieldPolynomialRing', 673
  `IsAbelianTom', 703
  `IsAdditiveElement', 296
  `IsAdditiveElementWithInverse', 296
  `IsAdditiveElementWithZero', 296
  `IsAdditiveGroup', 552
  `IsAdditiveGroupGeneralMapping', 308
  `IsAdditiveGroupHomomorphism', 308
  `IsAdditivelyCommutative', 553
  `IsAdditivelyCommutativeElement', 298
  `IsAdditivelyCommutativeElementCollColl', 298
  `Is\-Additively\-Commutative\-Element\-Collection', 298
  `IsAdditivelyCommutativeElementFamily', 298
  `IsAdditiveMagma', 551
  `IsAdditiveMagmaWithInverses', 552
  `IsAdditiveMagmaWithZero', 551
  `IsAlgebra', 613
  `IsAlgebraGeneralMapping', 309
  `IsAlgebraHomomorphism', 309
  `IsAlgebraicElement', 684
  `IsAlgebraicExtension', 683
  `IsAlgebraModuleElement', 625
  `IsAlgebraModuleElementCollection', 625
  `IsAlgebraModuleElementFamily', 625
  `IsAlgebraWithOne', 613
  `IsAlgebraWithOneGeneralMapping', 309
  `IsAlgebraWithOneHomomorphism', 309
  `IsAlphaChar', 250
  `IsAlternatingGroup', 413
  `IsAnticommutative', 561
  `IsAntisymmetricBinaryRelation', 312
  `IsAssociated', 562
  `IsAssociative', 320
  `IsAssociativeElement', 298
  `IsAssociativeElementCollColl', 298
  `IsAssociativeElementCollection', 298
  `IsAssocWord', 327
  `IsAssocWordWithInverse', 327
  `IsAssocWordWithOne', 327
  `IsAutomorphismGroup', 387
  `IsBasicWreathLessThanOrEqual', 330
  `IsBasicWreathProductOrdering', 282
  `IsBasis', 593
  `IsBasisByNiceBasis', 604
  `IsBasisOfAlgebraModuleElementSpace', 626
  `IsBergerCondition', 815
  `IsBijective', 303
  `IsBinaryRelation', 311
    \sub same as `IsEndoGeneralMapping', 311
  `IsBLetterAssocWordRep', 334
  `IsBLetterWordsFamily', 334
  `IsBlist', 207
  `IsBlockMatrixRep', 236
  `IsBool', 167
  `IsBound', for lists, 176
  IsBound and Unbind for Lists, \indexit{176}
  IsBound and Unbind for Records, \indexit{262}
  `IsBoundGlobal', 45
  `IsBrauerTable', 721
  `IsBravaisGroup', 429
  `IsBuiltFromAdditiveMagmaWithInverses', 342
  `IsBuiltFromGroup', 342
  `IsBuiltFromMagma', 342
  `IsBuiltFromMagmaWithInverses', 342
  `IsBuiltFromMagmaWithOne', 342
  `IsBuiltFromSemigroup', 342
  `IsCanonicalBasis', 596
  `IsCanonicalBasisFullMatrixModule', 600
  `IsCanonicalBasisFullRowModule', 600
  `IsCanonicalNiceMonomorphism', 385
  `IsCanonicalPcgs', 437
  `IsCentral', 320
  `IsChar', 246
  `IsCharacter', 767
  `IsCharacteristicSubgroup', 348
  `IsCharacterTable', 721
  `IsCharacterTableInProgress', 721
  `IsCharCollection', 246
  `IsCheapConwayPolynomial', 582
  `IsClassFunction', 758
  `IsClassFusionOfNormalSubgroup', 736
  `IsClosedStream', 97
  `IsCochain', 647
  `IsCochainCollection', 647
  `IsCollection', 264
  `IsCollectionFamily', 264
  `IsCommutative', 320
  `IsCommutativeElement', 298
  `IsCommutativeElementCollColl', 298
  `IsCommutativeElementCollection', 298
  `IsCompositionMappingRep', 301
  `IsConfluent', 340
    \sub for pc groups, 451
  `Is\-Conjugacy\-Class\-Subgroups\-By\-Stabilizer\-Rep', 369
  `IsConjugacyClassSubgroupsRep', 369
  `IsConjugate', 357
  `IsConjugatorAutomorphism', 386
  `IsConjugatorIsomorphism', 386
  `IsConstantRationalFunction', 665
  `IsConstantTimeAccessGeneralMapping', 309
  `IsConstantTimeAccessList', 171
  `IsContainedInSpan', 598
  `IsCopyable', 113
  `IsCyc', 156
  `IsCyclic', 362
    \sub for character tables, 727
  `IsCyclicTom', 703
  `IsCyclotomic', 156
  `IsCyclotomicField', 585
  `IsCyclotomicMatrixGroup', 428
  `IsDenseList', 170
  `IsDiagonalMat', 223
  `IsDigitChar', 250
  `IsDirectoryPath', 93
  `IsDistributive', 561
  `IsDivisionRing', 571
  `IsDomain', 288
  `IsDoneIterator', 275
  `IsDoubleCoset', 355
  `IsDuplicateFree', 191
  `IsDuplicateFreeList', 191
  `IsDxLargeGroup', 746
  `IsElementaryAbelian', 362
    \sub for character tables, 727
  `IsElementOfFpMonoid', 543
  `IsElementOfFpSemigroup', 543
  `IsElementOfFreeMagmaRing', 656
  `IsElementOfFreeMagmaRingCollection', 656
  `IsElementOfFreeMagmaRingFamily', 656
  `IsElementOfMagmaRingModuloRelations', 657
  `Is\-Element\-Of\-Magma\-Ring\-Modulo\-Relations\-Collection', 657
  `Is\-Element\-Of\-Magma\-Ring\-Modulo\-Relations\-Family', 657
  `Is\-Element\-Of\-Magma\-Ring\-Modulo\-Span\-Of\-Zero\-Family', 658
  `IsEmpty', 269
  `IsEmptyString', 249
  `IsEndOfStream', 100
  `IsEndoGeneralMapping', 309
    \sub same as `IsBinaryRelation', 311
  `IsEqualSet', 193
  `IsEquivalenceClass', 315
  `IsEquivalenceRelation', 312
  `IsEuclideanRing', 563
  `IsEvenInt', 127
  `IsExecutableFile', 93
  `IsExistingFile', 93
  `IsExtAElement', 296
  `IsExternalOrbit', 405
  `IsExternalSet', 404
  `IsExternalSubset', 405
  `IsExtLElement', 296
  `IsExtRElement', 296
  `IsFamilyPcgs', 449
  `IsFFE', 577
  `IsFFECollColl', 577
  `IsFFECollection', 577
  `IsField', 571
  `IsFieldControlledByGaloisGroup', 574
  `IsFieldHomomorphism', 309
  `IsFinite', 269
    \sub for character tables, 727
  `IsFiniteDimensional', 569
    \sub for matrix algebras, 614
  `IsFiniteFieldPolynomialRing', 673
  `IsFinitelyGeneratedGroup', 363
  `IsFiniteOrderElement', 298
  `IsFiniteOrderElementCollColl', 298
  `IsFiniteOrderElementCollection', 298
  `IsFiniteOrdersPcgs', 433
  `IsFixedStabilizer', 422
  `IsFLMLOR', 613
  `IsFLMLORWithOne', 613
  `IsFpGroup', 459
  `IsFpMonoid', 543
  `IsFpSemigroup', 543
  `IsFreeGroup', 328
  `IsFreeLeftModule', 569
  `IsFreeMagmaRing', 655
  `IsFreeMagmaRingWithOne', 655
  `IsFromFpGroupGeneralMappingByImages', 391
  `IsFromFpGroupHomomorphismByImages', 391
  `Is\-From\-Fp\-Group\-Std\-Gens\-General\-Mapping\-By\-Images', 391
  `Is\-From\-Fp\-Group\-Std\-Gens\-Homomorphism\-By\-Images', 391
  `IsFullHomModule', 603
  `IsFullMatrixModule', 570
  `IsFullRowModule', 570
  `Is\-Full\-Subgroup\-GLor\-SLRespecting\-Bilinear\-Form', 427
  `Is\-Full\-Subgroup\-GLor\-SLRespecting\-Quadratic\-Form', 428
  `Is\-Full\-Subgroup\-GLor\-SLRespecting\-Sesquilinear\-Form', 427
  `IsFullTransformationSemigroup', 534
  `IsFunction', 63
  `IsGaussianIntegers', 589
  `IsGaussianRationals', 584
  `IsGaussianSpace', 598
  `IsGaussInt', 158
  `IsGaussRat', 158
  `IsGeneralizedDomain', 288
  `IsGeneralizedRowVector', 182
  `IsGeneralLinearGroup', 426
  `IsGeneralMapping', 309
  `IsGeneralMappingFamily', 310
  `IsGeneratorsOf<Struct>', 285
  `IsGL', 426
  `IsGreensClass', 536
  `IsGreensDClass', 536
  `IsGreensDRelation', 536
  `IsGreensHClass', 536
  `IsGreensHRelation', 536
  `IsGreensJClass', 536
  `IsGreensJRelation', 536
  `IsGreensLClass', 536
  `IsGreensLessThanOrEqual', 536
  `IsGreensLRelation', 536
  `IsGreensRClass', 536
  `IsGreensRelation', 536
  `IsGreensRRelation', 536
  `IsGroup', 346
  `IsGroupGeneralMapping', 307
  `Is\-Group\-General\-Mapping\-By\-As\-Group\-General\-Mapping\-By\-Images', 391
  `IsGroupGeneralMappingByImages', 391
  `IsGroupGeneralMappingByPcgs', 391
  `IsGroupHClass', 537
  `IsGroupHomomorphism', 307
  `IsGroupOfAutomorphisms', 387
  `IsGroupRing', 655
  `IsHandledByNiceBasis', 570
    \sub for vector spaces, 604
  `IsHandledByNiceMonomorphism', 385
  `IsHasseDiagram', 312
  `IsHomogeneousList', 171
  `IsIdempotent', 291
  `IsIdenticalObj', 111
  `IsIncomparableUnder', 278
  `IsInducedFromNormalSubgroup', 817
  `IsInducedPcgs', 436
  `IsInducedPcgsWrtSpecialPcgs', 444
  `IsInfBitsFamily', 334
  `IsInfinity', 158
  `IsInjective', 303
  `IsInnerAutomorphism', 386
  `IsInputOutputStream', 105
  `IsInputStream', 97
  `IsInputTextNone', 97
  `IsInputTextStream', 97
  `IsInt', 127
  `IsIntegerMatrixGroup', 429
  `IsIntegers', 126
  `IsIntegralBasis', 596
  `IsIntegralCyclotomic', 156
  `IsIntegralRing', 560
  `IsInternallyConsistent', 115
    \sub for character tables, 736
    \sub for tables of marks, 704
  `IsIrreducibleCharacter', 767
  `IsIrreducibleRingElement', 562
  `IsIterator', 275
  `IsJacobianElement', 298
  `IsJacobianElementCollColl', 298
  `IsJacobianElementCollection', 298
  `IsJacobianRing', 561
  `IsLaurentPolynomial', 664
  `IsLaurentPolynomialDefaultRep', 680
  `IsLDistributive', 561
  `IsLeftAlgebraModuleElement', 625
  `IsLeftAlgebraModuleElementCollection', 625
  `IsLeftIdeal', 558
  `IsLeftIdealInParent', 558
  `IsLeftModule', 567
  `IsLeftModuleGeneralMapping', 308
  `IsLeftModuleHomomorphism', 308
  `IsLeftOperatorAdditiveGroup', 567
  `IsLeftSemigroupIdeal', 534
  `IsLeftVectorSpace', 590
  `IsLessThanOrEqualUnder', 278
  `IsLessThanUnder', 278
  `IsLetterAssocWordRep', 333
  `IsLetterWordsFamily', 333
  `IsLexicographicallyLess', 197
  `IsLieAbelian', 636
  `IsLieAlgebra', 613
  `IsLieMatrix', 220
  `IsLieNilpotent', 636
  `IsLieObject', 631
  `IsLieObjectCollection', 631
  `IsLieSolvable', 636
  `IsLinearMapping', 308
  `IsLinearMappingsModule', 603
  `IsList', 170
  `IsListDefault', 182
  `IsListOrCollection', 265
  `IsLowerAlphaChar', 250
  `IsLowerTriangularMat', 223
  `IsMagma', 316
  `IsMagmaHomomorphism', 306
  `IsMagmaRingModuloRelations', 657
  `IsMagmaRingModuloSpanOfZero', 658
  `IsMagmaWithInverses', 316
  `IsMagmaWithInversesIfNonzero', 316
  `IsMagmaWithOne', 316
  `IsMapping', 302
  `IsMatchingSublist', 190
  `IsMatrix', 219
  `IsMatrixGroup', 425
  `IsMatrixModule', 570
  `IsMatrixSpace', 598
  `IsMinimalNonmonomial', 820
  `IsModuloPcgs', 438
  `IsMonoid', 539
  `IsMonomial', for characters, 817
    \sub for character tables, 727
    \sub for groups, 817
    \sub for positive integers, 818
  `IsMonomialGroup', 362
  `IsMonomialMatrix', 223
  `IsMonomialNumber', 818
  `IsMonomialOrdering', 674
  `IsMultiplicativeElement', 296
  `IsMultiplicativeElementWithInverse', 297
  `IsMultiplicativeElementWithOne', 297
  `IsMultiplicativeElementWithZero', 297
  `IsMultiplicativeGeneralizedRowVector', 182
  `IsMultiplicativeZero', 320
  `IsMutable', 113
  `IsMutableBasis', 597
  `IsNaturalAlternatingGroup', 412
  `IsNaturalGL', 427
  `IsNaturalGLnZ', 429
  `IsNaturalSL', 427
  `IsNaturalSLnZ', 429
  `IsNaturalSymmetricGroup', 412
  `IsNearAdditiveElement', 296
  `IsNearAdditiveElementWithInverse', 296
  `IsNearAdditiveElementWithZero', 296
  `IsNearAdditiveGroup', 551
  `IsNearAdditiveMagma', 551
  `IsNearAdditiveMagmaWithInverses', 551
  `IsNearAdditiveMagmaWithZero', 551
  `IsNearlyCharacterTable', 721
  `IsNearRingElement', 297
  `IsNearRingElementWithInverse', 297
  `IsNearRingElementWithOne', 297
  `IsNegRat', 144
  `IsNilpotent', for character tables, 727
    \sub for groups with pcgs, 446
  `IsNilpotentElement', 643
  `IsNilpotentGroup', 362
  `IsNilpotentTom', 703
  `IsNonassocWord', 323
  `IsNonassocWordCollection', 323
  `IsNonassocWordWithOne', 323
  `IsNonassocWordWithOneCollection', 323
  `IsNonnegativeIntegers', 126
  `IsNonSPGeneralMapping', 310
  `IsNonTrivial', 269
  `IsNormal', 347
  `IsNormalBasis', 596
  `IsNotIdenticalObj', 112
  `IsNumberField', 585
  `IsObject', 110
  `IsOddInt', 127
  isomorphic, pc group, 452, 453
  `IsomorphicSubgroups', 389
  `IsomorphismFpAlgebra', 622
  `IsomorphismFpGroup', 468
    \sub for subgroups of fp groups, 470
  `IsomorphismFpGroupByGenerators', 468
  `IsomorphismFpGroupByGeneratorsNC', 468
  `IsomorphismFpGroupByPcgs', 450
  `IsomorphismFpSemigroup', 544
  `IsomorphismGroups', 389
  `IsomorphismMatrixAlgebra', 622
  `IsomorphismPcGroup', 453
  `IsomorphismPermGroup', 412
    \sub for Imf matrix groups, 530
  `IsomorphismPermGroupImfGroup', 531
  `IsomorphismReesMatrixSemigroup', 538
  `IsomorphismRefinedPcGroup', 452
  `Isomorphism<Rep><Struct>', 286
  isomorphisms, find all, 389
  `IsomorphismSCAlgebra', 623
  `IsomorphismSimplifiedFpGroup', 471
  `IsomorphismSpecialPcGroup', 453
  `IsomorphismTransformationSemigroup', 534
  `IsomorphismTypeInfoFiniteSimpleGroup', 363
  `IsOne', 291
  `IsOperation', 63
  `IsOrdering', 277
  `IsOrderingOnFamilyOfAssocWords', 279
  `IsOrdinaryMatrix', 219
  `IsOrdinaryTable', 721
  `IsOutputStream', 98
  `IsOutputTextNone', 98
  `IsOutputTextStream', 98
  `IsPadicExtensionNumber', 687
  `IsPadicExtensionNumberFamily', 687
  `IsParentPcgsFamilyPcgs', 449
  `IsPartialOrderBinaryRelation', 312
  `IsPcGroup', 450
  `IsPcGroupGeneralMappingByImages', 391
  `IsPcGroupHomomorphismByImages', 391
  `IsPcgs', 432
  `IsPcgsCentralSeries', 440
  `IsPcgsChiefSeries', 441
  `IsPcgsElementaryAbelianSeries', 440
  `IsPcgsPCentralSeriesPGroup', 441
  `IsPerfect', for character tables, 727
  `IsPerfectGroup', 362
  `IsPerfectTom', 703
  `IsPerm', 407
  `IsPermCollColl', 407
  `IsPermCollection', 407
  `IsPermGroup', 411
  `IsPermGroupGeneralMappingByImages', 391
  `IsPermGroupHomomorphismByImages', 391
  `IsPGroup', 363
  `IsPNilpotent', 364
  `IsPolycyclicGroup', 362
  `IsPolynomial', 664
  `IsPolynomialDefaultRep', 680
  `IsPolynomialFunction', 663
  `IsPolynomialFunctionsFamily', 678
  `IsPolynomialRing', 673
  `IsPosInt', 127
  `IsPositiveIntegers', 126
  `IsPosRat', 144
  `Is\-Preimages\-By\-As\-Group\-General\-Mapping\-By\-Images', 391
  `IsPreOrderBinaryRelation', 312
  `IsPrime', 562
  `IsPrimeField', 573
  `IsPrimeInt', 131
  `IsPrimeOrdersPcgs', 433
  `IsPrimePowerInt', 132
  `IsPrimitive', 403
  `IsPrimitiveCharacter', 816
  `IsPrimitivePolynomial', 665
  `IsPrimitiveRootMod', 138
  `IsProbablyPrimeInt', 131
  `IsPseudoCanonicalBasisFullHomModule', 603
  `IsPSolvable', 364
  `IsPSolvableCharacterTable', 736
  `IsPSolvableCharacterTableOp', 736
  `IsPurePadicNumber', 686
  `IsPurePadicNumberFamily', 686
  `IsQuasiPrimitive', 816
  `IsQuaternion', 614
  `IsQuaternionCollColl', 614
  `IsQuaternionCollection', 614
  `IsQuickPositionList', 205
  `IsQuotientSemigroup', 535
  `IsRange', 204
  `IsRat', 143
  `IsRationalFunction', 663
  `IsRationalFunctionDefaultRep', 680
  `IsRationalFunctionsFamily', 678
  `IsRationalMatrixGroup', 428
  `IsRationals', 143
  `IsRationalsPolynomialRing', 673
  `IsRDistributive', 561
  `IsReadableFile', 93
  `IsReadOnlyGlobal', 44
  `IsRecord', 258
  `IsRecordCollColl', 258
  `IsRecordCollection', 258
  `IsReduced', 341
  `IsReductionOrdering', 279
  `IsReesCongruence', 535
  `IsReesCongruenceSemigroup', 534
  `IsReesMatrixSemigroup', 537
  `IsReesMatrixSemigroupElement', 538
  `IsReesZeroMatrixSemigroup', 537
  `IsReesZeroMatrixSemigroupElement', 538
  `IsReflexiveBinaryRelation', 311
  `IsRegular', 402
  `IsRegularDClass', 537
  `IsRegularSemigroup', 533
  `IsRegularSemigroupElement', 533
  `IsRelativelySM', 819
  `IsRestrictedLieAlgebra', 641
  `IsRewritingSystem', 340
  `IsRightAlgebraModuleElement', 625
  `IsRightAlgebraModuleElementCollection', 625
  `IsRightCoset', 353
  `IsRightIdeal', 558
  `IsRightIdealInParent', 558
  `IsRightModule', 568
  `IsRightOperatorAdditiveGroup', 567
  `IsRightSemigroupIdeal', 534
  `IsRing', 555
  `IsRingElement', 297
  `IsRingElementWithInverse', 297
  `IsRingElementWithOne', 297
  `IsRingGeneralMapping', 309
  `IsRingHomomorphism', 309
  `IsRingWithOne', 559
  `IsRingWithOneGeneralMapping', 309
  `IsRingWithOneHomomorphism', 309
  `IsRootSystem', 638
  `IsRootSystemFromLieAlgebra', 638
  `IsRowModule', 570
  `IsRowSpace', 598
  `IsRowVector', 211
  `IsScalar', 297
  `IsSemiEchelonized', 599
  `IsSemigroup', 532
  `IsSemigroupCongruence', 535
  `IsSemigroupIdeal', 534
  `IsSemiRegular', 402
  `IsSet', 191
  `IsShortLexLessThanOrEqual', 330
  `IsShortLexOrdering', 280
  `IsSimple', for character tables, 727
  `IsSimpleAlgebra', 614
  `IsSimpleGroup', 362
  `IsSimpleSemigroup', 533
  `IsSingleValued', 302
  `IsSL', 427
  `IsSolvable', for character tables, 727
  `IsSolvableGroup', 362
  `IsSolvableTom', 703
  `IsSortedList', 191
  `IsSpecialLinearGroup', 427
  `IsSpecialPcgs', 443
  `IsSPGeneralMapping', 310
  `IsSporadicSimple', for character tables, 727
  `IsSSortedList', 191
  `IsStandardGeneratorsOfGroup', 709
  `IsStraightLineProgElm', 339
  `IsStraightLineProgram', 335
  `IsStream', 97
  `IsString', 246
  `IsStringRep', 249
  `Is<Struct>', 286
  `IsSubgroup', 347
  `IsSubgroupFpGroup', 459
  `IsSubgroupOfWholeGroupByQuotientRep', 471
  `IsSubgroupSL', 427
  `IsSubmonoidFpMonoid', 542
  `IsSubnormal', 348
  `IsSubnormallyMonomial', 819
  `IsSubsemigroupFpSemigroup', 542
  `IsSubset', 271
  `IsSubsetBlist', 208
  `IsSubsetLocallyFiniteGroup', 363
  `IsSubsetSet', 194
  `IsSubspacesVectorSpace', 592
  `IsSub<struct>', 288
  `IsSupersolvable', for character tables, 727
    \sub for groups with pcgs, 446
  `IsSupersolvableGroup', 362
  `IsSurjective', 303
  `IsSyllableAssocWordRep', 334
  `IsSyllableWordsFamily', 334
  `IsSymmetricBinaryRelation', 312
  `IsSymmetricGroup', 413
  `IsTable', 171
  `IsTableOfMarks', 699
  `IsTableOfMarksWithGens', 710
  `IsToPcGroupGeneralMappingByImages', 391
  `IsToPcGroupHomomorphismByImages', 391
  `IsToPermGroupGeneralMappingByImages', 391
  `IsToPermGroupHomomorphismByImages', 391
  `IsTotal', 302
  `IsTotalOrdering', 278
  `IsTransformation', 548
  `IsTransformationCollection', 548
  `IsTransformationMonoid', 534
  `IsTransformationSemigroup', 534
  `IsTransitive', for characters, 770
    \sub for class functions, 770
    \sub for group actions, 402
  `IsTransitiveBinaryRelation', 312
  `IsTranslationInvariantOrdering', 279
  `IsTrivial', 269
  `IsTuple', 300
  `IsTwoSidedIdeal', 558
  `IsTwoSidedIdealInParent', 558
  `IsUEALatticeElement', 650
  `IsUEALatticeElementCollection', 650
  `IsUEALatticeElementFamily', 650
  `IsUniqueFactorizationRing', 560
  `IsUnit', 561
  `IsUnivariatePolynomial', 664
  `IsUnivariatePolynomialRing', 673
  `IsUnivariateRationalFunction', 664
  `IsUnknown', 165
  `IsUpperAlphaChar', 250
  `IsUpperTriangularMat', 223
  `IsValidIdentifier', 42
  `IsVector', 297
  `IsVectorSpace', 590
  `IsVirtualCharacter', 767
  `IsWeightLexOrdering', 281
  `IsWeightRepElement', 651
  `IsWeightRepElementCollection', 651
  `IsWeightRepElementFamily', 651
  `IsWellFoundedOrdering', 278
  `IsWeylGroup', 639
  `IsWholeFamily', 270
  `IsWLetterAssocWordRep', 334
  `IsWLetterWordsFamily', 334
  `IsWord', 322
  `IsWordCollection', 323
  `IsWordWithInverse', 322
  `IsWordWithOne', 322
  `IsWreathProductOrdering', 282
  `IsWritableFile', 93
  `IsZero', 291
  `IsZeroGroup', 534
  `IsZeroSimpleSemigroup', 533
  `IsZeroSquaredElement', 299
  `IsZeroSquaredElementCollColl', 299
  `IsZeroSquaredElementCollection', 299
  `IsZeroSquaredRing', 561
  `IsZmodnZObj', 135
  `IsZmodnZObjNonprime', 135
  `IsZmodpZObj', 135
  `IsZmodpZObjLarge', 135
  `IsZmodpZObjSmall', 135
  `Iterated', 202
  `Iterator', 274
  `IteratorByBasis', 595
  `IteratorByFunctions', 276
  `IteratorList', 276
  Iterators, \indexit{274}
  `IteratorSorted', 275
\letter J
  $j_N$, 160
  `Jacobi', 138
  `JenningsLieAlgebra', 642
  `JenningsSeries', 367
  `JoinEquivalenceRelations', 314
  `JoinStringsWithSeparator', 252
  `JordanDecomposition', 231
\letter K
  $k_N$, 160
  `KappaPerp', 643
  `KB_REW', 546
  `KernelOfAdditiveGeneralMapping', 308
  `KernelOfCharacter', 769
  `KernelOfMultiplicativeGeneralMapping', 307
  `KernelOfTransformation', 549
  Keywords, \indexit{41}
  `KillingMatrix', 643
  `KnownAttributesOfObject', 121
  Known Problems of the Configure Process, \indexit{828}
  `KnownPropertiesOfObject', 124
  `KnownTruePropertiesOfObject', 124
  `KnowsHowToDecompose', 379
  `KnuthBendixRewritingSystem', 547
  Krasner-Kaloujnine theorem, 503
  `KroneckerProduct', 225
  `KuKGenerators', 503
\letter L
  $l_N$, 160
  `Lambda', 136
  Language Overview, \indexit{39}
  larger or equal, 47
  larger test, 47
  `LargestElementGroup', 375
  `LargestElementStabChain', 420
  `LargestMovedPoint', 408
  `LargestUnknown', 165
  `last', 64
  `LastSystemError', 90
  `LaTeXStringDecompositionMatrix', 734
  lattice base reduction, 242, 243
  lattice basis reduction, for virtual characters, 774
  `LatticeByCyclicExtension', 372
  `LatticeGeneratorsInUEA', 650
  Lattice Reduction, \indexit{242}
  `LatticeSubgroups', 370
  `LatticeSubgroupsByTom', 697
  `LaurentPolynomialByCoefficients', 670
  `LaurentPolynomialByExtRep', 681
  Laurent Polynomials, \indexit{670}
  `LClassOfHClass', 536
  `Lcm', 565
  `LcmInt', 130
  `LcmOp', 565
  `LeadCoeffsIGS', 437
  `LeadingCoefficient', 666
  `LeadingCoefficientOfPolynomial', 674
  `LeadingExponentOfPcElement', 434
  `LeadingMonomial', 667
  `LeadingMonomialOfPolynomial', 674
  `LeadingTermOfPolynomial', 674
  Leaving GAP, \indexit{73}
  `LeftActingAlgebra', 626
  `LeftActingDomain', 568
  `LeftActingRingOfIdeal', 559
  `LeftAlgebraModule', 624
  `LeftAlgebraModuleByGenerators', 624
  left cosets, 353
  `LeftDerivations', 633
  `LeftIdeal', 557
  `LeftIdealByGenerators', 558
  `LeftIdealNC', 558
  `LeftModuleByGenerators', 568
  `LeftModuleByHomomorphismToMatAlg', 627
  `LeftModuleGeneralMappingByImages', 601
  `LeftModuleHomomorphismByImages', 601
  `LeftModuleHomomorphismByImagesNC', 601
  `LeftModuleHomomorphismByMatrix', 602
  `LeftQuotient', 293
    \sub for words, 331
  `LeftShiftRowVector', 215
  legacy, 840
  `Legendre', 139
  `Length', 191
    \sub of an associative word, 331
  length, of a word, 331
  `LengthsTom', 700
  `LenstraBase', 587
  `LessThanFunction', 278
  `LessThanOrEqualFunction', 278
  `LetterRepAssocWord', 334
  `LevelsOfGenerators', 282
  `LeviMalcevDecomposition', 619
    \sub for Lie algebras, 637
  Lexical Structure, \indexit{40}
  `LexicographicOrdering', 279
  `LGFirst', 444
  `LGLayers', 444
  `LGLength', 444
  `LGWeights', 443
  library tables, 718
  `LieAlgebra', 632
  `LieAlgebraByStructureConstants', 632
  `LieBracket', 293
  `LieCenter', 634
  `LieCentralizer', 634
  `LieCentre', 634
  `LieCoboundaryOperator', 647
  `LieDerivedSeries', 635
  `LieDerivedSubalgebra', 635
  `LieFamily', 632
  `LieLowerCentralSeries', 636
  `LieNilRadical', 635
  `LieNormalizer', 634
  `LieObject', 631
  Lie objects, \indexit{631}
  `LieSolvableRadical', 635
  `LieUpperCentralSeries', 636
  `LiftedInducedPcgs', 439
  `LiftedPcElement', 439
  `LinearAction', 445
  `LinearActionLayer', 445
  `LinearCharacters', 726
  `LinearCombination', 595
  `LinearCombinationPcgs', 434
  Linear equations over the integers and Integral Matrices, \indexit{237}
  `LinearIndependentColumns', 242
  Linear Mappings, \indexit{308}
  `LinearOperation', 445
  `LinearOperationLayer', 445
  Line Editing, \indexit{73}
  `LinesOfStraightLineProgram', 336
  `List', 199
  list and non-list, difference, 184
    \sub left quotient, 186
    \sub mod, 186
    \sub product, 185
    \sub quotient, 186
  List Assignment, \indexit{174}
  list assignment, operation, 172
  `ListBlist', 208
  list boundedness test, operation, 172
  List Categories, \indexit{170}
  list element, access, 172
    \sub assignment, 174
    \sub operation, 172
  List Elements, \indexit{172}
  list equal, comparison, 180
  `ListN', 202
  list of available books, 23
  `ListPerm', 410
  Lists and Collections, \indexit{265}
  list smaller, comparison, 181
  `ListStabChain', 420
  list unbind, operation, 172
  `ListWithIdenticalEntries', 187
  `ListX', 202
  `LLL', 774
  LLL algorithm, for Gram matrices, 243
    \sub for vectors, 242
    \sub for virtual characters, 774
  `LLLReducedBasis', 242
  `LLLReducedGramMat', 243
  `LoadDynamicModule', 35
  Loading a GAP Package, \indexit{836}
  loading a saved workspace, 37
  `LoadPackage', 836
  `local', 55
  logarithm, discrete, 138
    \sub of a root of unity, 158
  `LogFFE', 579
  logical, 167
  logical operations, 168
  `LogInt', 128
  `LogMod', 137
  `LogModShanks', 137
  `LogTo', 95
    \sub for streams, 102
    \sub stop logging, 95
  `LongestWeylWordPerm', 640
  loop, read eval print, 64
  loop, `for', 53
    \sub `repeat', 52
    \sub `while', 52
  loop over iterator, 54
  loop over object, 54
  loop over range, 53
  loops, leaving, 55
    \sub restarting, 55
  `LowercaseString', 251
  `LowerCentralSeriesOfGroup', 366
  Low Index Subgroups, \indexit{467}
  `LowIndexSubgroupsFpGroup', 467
  Low Level Routines to Modify and Create Stabilizer Chains, \indexit{421}
  `Lucas', 153
\letter M
  $m_N$, 160
  Macintosh, 831, 832
  MacOS, 832
  `Magma', 317
  `MagmaByGenerators', 317
  `MagmaByMultiplicationTable', 318
  Magma Categories, \indexit{316}
  `MagmaElement', 318
  Magma Generation, \indexit{317}
  `MagmaHomomorphismByFunctionNC', 306
  Magma Homomorphisms, \indexit{306}
  `MagmaRingModuloSpanOfZero', 658
  Magma Rings modulo Relations, \indexit{657}
  Magma Rings modulo the Span of a Zero Element, \indexit{658}
  Magmas Defined by Multiplication Tables, \indexit{318}
  `MagmaWithInverses', 317
  `MagmaWithInversesByGenerators', 317
  `MagmaWithInversesByMultiplicationTable', 318
  `MagmaWithOne', 317
  `MagmaWithOneByGenerators', 317
  `MagmaWithOneByMultiplicationTable', 318
  Main Loop, \indexit{64}
  `MakeConfluent', 341
  `MakeImmutable', 113
  `MakeReadOnlyGlobal', 44
  `MakeReadWriteGlobal', 44
  Making transformation semigroups, \indexit{534}
  Manual Conventions, \indexit{20}
  map, parametrized, 801
  `MappedWord', 324
  `MappingByFunction', 301
  `MappingPermListList', 410
  Mappings that Respect Addition, \indexit{308}
  Mappings that Respect Multiplication, \indexit{307}
  Mappings which are Compatible with Algebraic Structures, \indexit{306}
  maps, 792
  `MarksTom', 700
  `MatAlgebra', 610
  `MatClassMultCoeffsCharTable', 738
  `MathieuGroup', 506
  `MatLieAlgebra', 633
  matrices, commutator, 222
  Matrices as Basis of a Row Space, \indexit{230}
  Matrices as Linear Mappings, \indexit{231}
  Matrices over Finite Fields, \indexit{232}
  Matrices Representing Linear Equations and the Gaussian Algorithm, \indexit{226}
  `MatrixAlgebra', 610
  `MatrixAutomorphisms', 754
  matrix automorphisms, 795
  `MatrixByBlockMatrix', 236
  Matrix Constructions, \indexit{224}
  Matrix Groups in Characteristic 0, \indexit{428}
  `MatrixLieAlgebra', 633
  `MatrixOfAction', 626
  matrix spaces, 598
  `MatScalarProducts', 768
  `MatTom', 702
  `MaximalAbelianQuotient', 368
  `MaximalBlocks', 403
  `MaximalNormalSubgroups', 370
  `MaximalSubgroupClassReps', 369
  `MaximalSubgroups', 369
    \sub for groups with pcgs, 446
  `MaximalSubgroupsLattice', 371
  `MaximalSubgroupsTom', 706
  `Maximum', 197
  `MaximumList', 198
  MeatAxe Modules, \indexit{688}
  `MeetEquivalenceRelations', 314
  `MeetMaps', 804
  Membership Test for Collections, \indexit{273}
  Membership Test for Lists, \indexit{180}
  `MinimalElementCosetStabChain', 420
  `MinimalGeneratingSet', 375
    \sub for groups with pcgs, 446
  `MinimalNonmonomialGroup', 820
  Minimal Nonmonomial Groups, \indexit{820}
  `MinimalNormalSubgroups', 370
  `MinimalPolynomial', 668
    \sub over a field, 574
    \sub over a ring, 668
  Minimal Polynomials, \indexit{668}
  `MinimalStabChain', 418
  `MinimalSupergroupsLattice', 371
  `MinimalSupergroupsTom', 707
  `MinimizedBombieriNorm', 670
  `Minimum', 197
  `MinimumList', 198
  `MinusCharacter', 810
  Miscellaneous, \indexit{142}
  Miscellaneous Name Changes or Removed Names, \indexit{841}
  mod, integers, 135
    \sub laurent polynomials, 662
    \sub lists, 186
    \sub rationals, 48
  `mod', 48
    \sub arithmetic operators, 48
    \sub for character tables, 725
    \sub residue class rings, 134
  modular inverse, 48
  modular remainder, 48
  modular roots, 140
  `ModuleByRestriction', 628
  Module Constructions, \indexit{688}
  Module Homomorphisms, \indexit{691}
  `ModuleOfExtension', 455
  Modules over Lie Algebras and Their Cohomology, \indexit{646}
  Modules over Semisimple Lie Algebras, \indexit{648}
  modulo, 48
    \sub arithmetic operators, 48
    \sub for pcgs, 438
    \sub residue class rings, 134
  `ModuloPcgs', 438
  `MoebiusMu', 141
  `MoebiusTom', 702
  Molien Series, \indexit{781}
  `MolienSeries', 781
  `MolienSeriesInfo', 782
  `MolienSeriesWithGivenDenominator', 783
  `Monoid', 539
  `MonoidByGenerators', 539
  `MonoidByMultiplicationTable', 540
  `MonoidOfRewritingSystem', 547
  `MonomialComparisonFunction', 674
  `MonomialExtGrlexLess', 677
  `MonomialExtrepComparisonFun', 675
  `MonomialGrevlexOrdering', 675
  `MonomialGrlexOrdering', 675
  `MonomialLexOrdering', 675
  Monomial Orderings, \indexit{674}
  `MonomialTotalDegreeLess', 841
  monomorphisms, find all, 389
  `MorClassLoop', 389
  More about Boolean Lists, \indexit{210}
  More About Global Variables, \indexit{44}
  More about Tables of Marks, \indexit{694}
  `MostFrequentGeneratorFpGroup', 465
  `MovedPoints', 409
  Moved Points of Permutations, \indexit{408}
  `MTX.BasesCompositionSeries', 690
  `MTX.BasesMaximalSubmodules', 690
  `MTX.BasesMinimalSubmodules', 689
  `MTX.BasesMinimalSupermodules', 690
  `MTX.BasesSubmodules', 689
  `MTX.BasisInOrbit', 691
  `MTX.BasisRadical', 690
  `MTX.BasisSocle', 690
  `MTX.CollectedFactors', 690
  `MTX.CompositionFactors', 690
  `MTX.DegreeSplittingField', 689
  `MTX.Dimension', 689
  `MTX.Distinguish', 691
  `MTX.Field', 689
  `MTX.Generators', 689
  `MTX.Homomorphism', 691
  `MTX.Homomorphisms', 691
  `MTX.InducedAction', 690
  `MTX.InducedActionFactorMatrix', 690
  `MTX.InducedActionFactorModule', 690
  `MTX.InducedActionMatrix', 690
  `MTX.InducedActionMatrixNB', 690
  `MTX.InducedActionSubmodule', 690
  `MTX.InducedActionSubmoduleNB', 690
  `MTX.InvariantBilinearForm', 691
  `MTX.InvariantQuadraticForm', 691
  `MTX.InvariantSesquilinearForm', 691
  `MTX.IsAbsolutelyIrreducible', 689
  `MTX.IsEquivalent', 691
  `MTX.IsIrreducible', 689
  `MTX.Isomorphism', 691
  `MTX.NormedBasisAndBaseChange', 690
  `MTX.OrthogonalSign', 691
  `MTX.ProperSubmoduleBasis', 689
  `MTX.SubGModule', 689
  `MTX.SubmoduleGModule', 689
  multiplication, 48
    \sub matrices, 221
    \sub matrix and matrix list, 222
    \sub matrix and scalar, 220
    \sub matrix and vector, 221
    \sub operation, 293
    \sub scalar and matrix, 220
    \sub scalar and matrix list, 222
    \sub scalar and vector, 212
    \sub vector and matrix, 221
    \sub vector and matrix list, 222
    \sub vector and scalar, 212
    \sub vectors, 212
  `MultiplicationTable', 318
  Multiplicative Arithmetic for Lists, \indexit{184}
  Multiplicative Arithmetic Functions, \indexit{140}
  `MultiplicativeNeutralElement', 320
  multiplicative order of an integer, 137
  `MultiplicativeZero', 320
  `MultiplicativeZeroOp', 290
  multiplicity, of constituents of a group character, 768
  multiplier, 378
  multisets, 193
  Multivariate Polynomials, \indexit{667}
  `MultRowVector', 215
  Murnaghan components, 780, 781
  Mutability and Copyability, \indexit{112}
  Mutability Status and List Arithmetic, \indexit{187}
  Mutable Bases, \indexit{597}
  `MutableBasis', 597
  `MutableBasisOfClosureUnderAction', 616
  `Mutable\-Basis\-Of\-Ideal\-In\-Nonassociative\-Algebra', 617
  `MutableBasisOfNonassociativeAlgebra', 617
  `MutableCopyMat', 225
  `MutableIdentityMat', 225
  `MutableNullMat', 225
\letter N
  $n_k$, 161
  `Name', 115
  `NameFunction', 61
  `NameRNam', 263
  `NamesFilter', 118
  `NamesGVars', 45
  `NamesLocalVariablesFunction', 61
  `NamesOfFusionSources', 799
  `NamesSystemGVars', 45
  `NamesUserGVars', 45
  `NaturalCharacter', 766
  Natural Embeddings related to Magma Rings, \indexit{656}
  `NaturalHomomorphismByGenerators', 306
  `NaturalHomomorphismByIdeal', 622
  `NaturalHomomorphismByNormalSubgroup', 368
  `NaturalHomomorphismByNormalSubgroupNC', 368
  `NaturalHomomorphismBySubAlgebraModule', 629
  `NaturalHomomorphismBySubspace', 602
  `NearAdditiveGroup', 552
  `NearAdditiveGroupByGenerators', 552
  `NearAdditiveMagma', 552
  `NearAdditiveMagmaByGenerators', 552
  `NearAdditiveMagmaWithZero', 552
  `NearAdditiveMagmaWithZeroByGenerators', 552
  `NearlyCharacterTablesFamily', 722
  negative number, 48
  `NegativeRoots', 638
  `NegativeRootVectors', 638
  `NestingDepthA', 182
  `NestingDepthM', 183
  `NewInfoClass', 79
  newline, 41
  newline character, 248
  `NewmanInfinityCriterion', 475
  New Presentations and Presentations for Subgroups, \indexit{470}
  `NextIterator', 275
  `NextPrimeInt', 132
  `NF', 584
  `NiceBasis', 604
  `NiceBasisFiltersInfo', 605
  `NiceFreeLeftModule', 604
  `NiceFreeLeftModuleInfo', 604
  `NiceMonomorphism', 385
  `NiceMonomorphismAutomGroup', 388
  Nice Monomorphisms, \indexit{385}
  `NiceObject', 385
  `NiceVector', 604
  `NilpotencyClassOfGroup', 362
  `NilpotentQuotientOfFpLieAlgebra', 645
  `NK', 161
  `NOAUTO', 837
  `NonnegativeIntegers', 126
  `NonnegIntScalarProducts', 806, 807
  `NonNilpotentElement', 643
  `Norm', 574
    \sub of character, 768
  `NormalBase', 576
  `NormalClosure', 358
  `NormalFormIntMat', 240
  Normal Forms of Integer Matrices - Name Changes, \indexit{841}
  Normal Forms over the Integers, \indexit{238}
  `NormalIntersection', 358
  `Normalized\-Element\-Of\-Magma\-Ring\-Modulo\-Relations', 657
  `NormalizedWhitespace', 252
  `Normalizer', 357
  normalizer, 357
  `NormalizerInGLnZ', 429
  `NormalizerInGLnZBravaisGroup', 429
  `NormalizersTom', 704
  `NormalizerTom', 704
  `NormalizeWhitespace', 252
  `NormalSeriesByPcgs', 442
  Normal Structure, \indexit{357}
  `NormalSubgroupClasses', 756
  `NormalSubgroupClassesInfo', 756
  `NormalSubgroups', 370
  `NormedRowVector', 213
  `NormedRowVectors', 601
  `NormedVectors', 841
  `not', 169
  `NrArrangements', 148
  `NrBasisVectors', 597
  `NrCombinations', 147
  `NrConjugacyClasses', 356
    \sub for character tables, 727
  `NrConjugacyClassesGL', 510
  `NrConjugacyClassesGU', 510
  `NrConjugacyClassesPGL', 510
  `NrConjugacyClassesPGU', 510
  `NrConjugacyClassesPSL', 510
  `NrConjugacyClassesPSU', 510
  `NrConjugacyClassesSL', 510
  `NrConjugacyClassesSLIsogeneous', 510
  `NrConjugacyClassesSU', 510
  `NrConjugacyClassesSUIsogeneous', 510
  `NrDerangements', 150
  `NrInputsOfStraightLineProgram', 336
  `NrMovedPoints', 409
  `NrOrderedPartitions', 152
  `NrPartitions', 151
  `NrPartitionsSet', 150
  `NrPartitionTuples', 153
  `NrPermutationsList', 149
  `NrPolyhedralSubgroups', 737
  `NrPrimitiveGroups', 521
  `NrRestrictedPartitions', 152
  `NrSubsTom', 700
  `NrTransitiveGroups', 512
  `NrTuples', 149
  `NrUnorderedTuples', 148
  `NullAlgebra', 611
  `NullMat', 224
  `NullspaceIntMat', 237
  `NullspaceMat', 226
  `NullspaceMatDestructive', 226
  `NullspaceModQ', 235
  `Number', 199
  number, Bell, 146
    \sub binomial, 145
    \sub Stirling, of the first kind, 146
    \sub Stirling, of the second kind, 147
  `NumberArgumentsFunction', 61
  `NumberFFVector', 214
  number field, 585
  number fields, Galois group, 588
  `NumberIrreducibleSolvableGroups', 523
  `NumberPerfectGroups', 517
  `NumberPerfectLibraryGroups', 517
  `NumberSmallGroups', 514
  `NumberSyllables', 332
  numerator, of a rational, 144
  `NumeratorOfModuloPcgs', 438
  `NumeratorOfRationalFunction', 663
  `NumeratorRat', 144
  Numerical Group Attributes, \indexit{364}
\letter O
  $O_p(G)$, see `PCore', 357
  `ObjByExtRep', 650
  Objects, \indexit{110}
  obsolete, 840
  `OCOneCocycles', 377
  octal character codes, 248
  `OctaveAlgebra', 610
  `od', 53
  `OldGeneratorsOfPresentation', 492
  `Omega', 361
  `ONanScottType', 413
  `OnBreak', 68
  `OnBreakMessage', 69
  `One', 289
  `OneAttr', 289
  `OneCoboundaries', 376
  `OneCocycles', 376
  one cohomology, 375
  `OneFactorBound', 670
  `OneImmutable', 289
  `OneIrreducibleSolvableGroup', 523
  `One<Library>Group', 512
  `OneMutable', 289
  `OneOfPcgs', 433
  `OneOp', 289
  `OnePrimitiveGroup', 512
  `OneSameMutability', 289
  `OneSM', 289
  `OneSmallGroup', 514
  `OneTransitiveGroup', 512
  `OnIndeterminates', 668
    \sub as a permutation action, 394
  `OnLeftInverse', 393
  `OnLines', 394
    \sub example, 507
  `OnPairs', 393
  `OnPoints', 393
  `OnRight', 393
  `OnSets', 393
  `OnSetsDisjointSets', 394
  `OnSetsSets', 393
  `OnSetsTuples', 394
  `OnSubspacesByCanonicalBasis', 395
  `OnTuples', 393
  `OnTuplesSets', 394
  `OnTuplesTuples', 394
  `Operation', 840
  `OperationAlgebraHomomorphism', 622
  Operational Structure of Domains, \indexit{283}
  `OperationHomomorphism', 840
  operations, for booleans, 168
  Operations and Attributes for Vector Spaces, \indexit{591}
  Operations applicable to All Streams, \indexit{98}
  Operations Concerning Blocks, \indexit{732}
  Operations for (Near-)Additive Magmas, \indexit{554}
  Operations for Abelian Number Fields, \indexit{584}
  operations for algebraic elements, 683
  Operations for Associative Words, \indexit{331}
  Operations for Associative Words by their Syllables, \indexit{332}
  Operations for Booleans, \indexit{168}
  Operations for Brauer Characters, \indexit{790}
  Operations for Class Functions, \indexit{767}
  Operations for Collections, \indexit{271}
  Operations for Cyclotomics, \indexit{155}
  Operations for Domains, \indexit{288}
  Operations for Finite Field Elements, \indexit{578}
  Operations for Finitely Presented Groups, \indexit{461}
  Operations for Group Homomorphisms, \indexit{382}
  Operations for Input Streams, \indexit{99}
  Operations for Lists, \indexit{195}
  Operations for Output Streams, \indexit{101}
  Operations for Pc Groups, \indexit{453}
  Operations for Rational Functions, \indexit{662}
  Operations for Special Kinds of Bases, \indexit{596}
  Operations for Stabilizer Chains, \indexit{419}
  Operations for Vector Space Bases, \indexit{594}
  Operations for Words, \indexit{324}
  Operations on elements of the algebra, \indexit{341}
  Operations on rewriting systems, \indexit{340}
  Operations to Evaluate Strings, \indexit{254}
  Operations to Produce or Manipulate Strings, \indexit{251}
  Operations which have Special Methods for Groups with Pcgs, \indexit{446}
  operators, 42
    \sub arithmetic, 48
    \sub associativity, 49
    \sub for cyclotomics, 159
    \sub for lists, 181
    \sub precedence, 48, 49
  Operators for Character Tables, \indexit{725}
  Operators for Matrices, \indexit{220}
  Operators for Row Vectors, \indexit{211}
  Optimization and Compiler Options, \indexit{829}
  options, 27, 821
    \sub command line, filenames, 29
    \sub command line, internal, 30
  options, under UNIX, 27
  `or', 168
  `Orbit', 395
  `OrbitFusions', 800
  `OrbitLength', 396
  `OrbitLengths', 396
  `OrbitLengthsDomain', 396
  `OrbitPerms', 411
  `OrbitPowerMaps', 795
  `Orbits', operation/attribute, 396
  Orbits, \indexit{395}
  `OrbitsDomain', 396
  `OrbitsPerms', 411
  `OrbitStabChain', 420
  `OrbitStabilizer', 397
  `OrbitStabilizerAlgorithm', 397
  Orbit Stabilizer Methods for Polycyclic Groups, \indexit{446}
  `Order', 292
    \sub of a class function, 764
  order,  of a group, 345
    \sub of a list, collection or domain, 270
    \sub of the prime residue group, 136
  `OrderedPartitions', 151
  ordering, booleans, 168
    \sub of records, 262
  `OrderingByLessThanFunctionNC', 277
  `OrderingByLessThanOrEqualFunctionNC', 277
  `OrderingOfRewritingSystem', 340
  `OrderingOnGenerators', 279
  `OrderingsFamily', 277
  Orderings on families of associative words, \indexit{279}
  `OrderMod', 137
  `OrderOfRewritingSystem', 340
  `OrdersClassRepresentatives', 728
  `OrdersTom', 700
  `Ordinal', 255
  ordinary character, 767
  `OrdinaryCharacterTable', 727
  `OrthogonalComponents', 780
  Orthogonal Embeddings, \indexit{244}
  `OrthogonalEmbeddings', 244
  `OrthogonalEmbeddingsSpecialDimension', 776
  OSX, 831
  Other Filters, \indexit{125}
  Other Operations Applicable to any Object, \indexit{115}
  Other Operations for Character Tables, \indexit{736}
  Other Operations for Tables of Marks, \indexit{704}
  output, suppressing, 64
  `OutputLogTo', 95
    \sub for streams, 102
    \sub stop logging output, 95
  `OutputTextFile', 103
  `OutputTextNone', 106
  `OutputTextString', 104
  `OutputTextUser', 104
\letter P
  $p$-group, 363
  package, 836
  Package Interface - Obsolete Functions and Name Changes, \indexit{840}
  Packages, \indexit{825}
  `PadicCoefficients', 242
  `PadicExtensionNumberFamily', 686
  `PadicNumber', 686
    \sub for pure padics, 685
  `PadicValuation', 563
  `Pager', 25
  `Parametrized', 803
  Parametrized Maps, \indexit{801}
  parametrized maps, 792
  `Parent', 287
  `ParentPcgs', 436
  Parents, \indexit{287}
  `PartialFactorization', 133
  partial order, 312
  `PartialOrderByOrderingFunction', 313
  `PartialOrderOfHasseDiagram', 312
  `Partitions', 151
  partitions, improper, of an integer, 152
    \sub ordered, of an integer, 152
    \sub restricted, of an integer, 152
  `PartitionsGreatestEQ', 152
  `PartitionsGreatestLE', 152
  `PartitionsSet', 150
  `PartitionTuples', 153
  `PcElementByExponents', 434
  `PcElementByExponentsNC', 434
  `PCentralLieAlgebra', 642
  `PCentralNormalSeriesByPcgsPGroup', 441
  `PCentralSeries', 367
  `PcGroupCode', 457
  `PcGroupCodeRec', 457
  `PcGroupFpGroup', 450
  Pc groups versus fp groups, \indexit{450}
  `PcGroupWithPcgs', 452
  `Pcgs', 432
  `Pcgs_OrbitStabilizer', 446
  Pcgs and Normal Series, \indexit{440}
  `PcgsByPcSequence', 432
  `PcgsByPcSequenceNC', 432
  `PcgsCentralSeries', 440
  `PcgsChiefSeries', 441
  `PcgsElementaryAbelianSeries', 440
  `PcgsPCentralSeriesPGroup', 441
  `PClassPGroup', 364
  `PCore', 357
  `PcSeries', 433
  `PerfectGroup', 516
  perfect groups, 516
  `PerfectIdentification', 517
  `PerfectResiduum', 359
  `Perform', 197
  `Permanent', 154
  Permanent of a Matrix, \indexit{154}
  `PermBounds', 789
  `PermCharInfo', 784
  `PermCharInfoRelative', 785
  `PermChars', 786
  `PermCharsTom', 713
  `PermComb', 789
  `PermLeftQuoTransformation', 550
  `PermList', 410
  `PermListList', 197
  `Permutation', 401
  `PermutationCharacter', 767
  permutation character, 812
  permutation characters, possible, 783, 786
  `PermutationCycle', 401
  `PermutationCycleOp', 401
  `PermutationMat', 224
  `PermutationsFamily', 407
  Permutations Induced by Elements and Cycles, \indexit{401}
  `PermutationsList', 149
  `PermutationTom', 699
  `Permuted', 198
    \sub as a permutation action, 395
    \sub for class functions, 764
  `PGL', 509
  `PGU', 509
  `Phi', 136
  point stabilizer, 397
  Polycyclic Generating Systems, \indexit{431}
  `PolynomialByExtRep', 681
  `PolynomialCoefficientsOfPolynomial', 666
  `PolynomialDivisionAlgorithm', 676
  Polynomial Factorization, \indexit{668}
  `PolynomialModP', 669
  `PolynomialReducedRemainder', 676
  `PolynomialReduction', 676
  `PolynomialRing', 671
  Polynomial Rings, \indexit{671}
  Polynomials as Univariate Polynomials in one Indeterminate, \indexit{666}
  polynomials over abelian number fields, factors, 584
  Polynomials over the Rationals, \indexit{669}
  `PopOptions', 88
  Portability, \indexit{90}
  Porting GAP, \indexit{830}
  `Position', 188
  `PositionBound', 189
  `PositionCanonical', 188
  `PositionFirstComponent', 190
  `PositionNonZero', 190
  `PositionNot', 190
  `PositionNthOccurrence', 188
  `PositionProperty', 189
  `PositionSet', 189
  `PositionSorted', 188
  `PositionStream', 100
  `PositionSublist', 190
  `PositionWord', 331
  `PositiveIntegers', 126
  positive number, 48
  `PositiveRoots', 638
  `PositiveRootVectors', 638
  `PossibleClassFusions', 799
  `PossibleFusionsCharTableTom', 712
  Possible Permutation Characters, \indexit{783}
  possible permutation characters, 783, 786
  `PossiblePowerMaps', 793
  power, 48
    \sub matrix, 221
    \sub meaning for class functions, 763
    \sub of words, 331
  `PowerMap', 793
  `PowerMapByComposition', 795
  `PowerMapOp', 793
  Power Maps, \indexit{792}
  `PowerMapsAllowedBySymmetrizations', 810
  `PowerMod', 565
  `PowerModCoeffs', 217
  `PowerModInt', 131
  `PowerPartition', 153
  powerset, 147
  `PowerSubalgebraSeries', 615
  `PQuotient', 472
  precedence, 48
  precedence test, for permutations, 408
  `PrefrattiniSubgroup', 359
    \sub for groups with pcgs, 446
  `PreImage', 305
  `PreImageElm', 305
  `PreImages', 305
  `PreImagesElm', 304
  Preimages in the Free Group, \indexit{460}
  Preimages in the Free Semigroup, \indexit{544}
  `PreimagesOfTransformation', 549
  `PreImagesRange', 304
  `PreImagesRepresentative', 305
  `PreImagesSet', 305
  Preimages under Homomorphisms from an FpGroup, \indexit{471}
  Preimages under Mappings, \indexit{304}
  preorder, 312
  `PresentationFpGroup', 476
  `PresentationNormalClosure', 481
  `PresentationNormalClosureRrs', 481
  `PresentationSubgroup', 479
  `PresentationSubgroupMtc', 480
  `PresentationSubgroupRrs', 479
  `PresentationViaCosetTable', 477
  previous result, 64
  `PrevPrimeInt', 132
  `PrimaryGeneratorWords', 480
  primary subgroup generators, 494
  `PrimeBlocks', 732
  `PrimeBlocksOp', 732
  `PrimeField', 573
  Prime Integers and Factorization, \indexit{131}
  `PrimePGroup', 364
  `PrimePowersInt', 134
  prime residue group, 136
    \sub exponent, 137
    \sub generator, 138
    \sub order, 136
  Prime Residues, \indexit{136}
  `PrimeResidues', function, 136
  `Primes', 131
  primitive, 403
  `PRIMITIVE_INDICES_MAGMA', 522
  `PrimitiveElement', 573
  `PrimitiveGroup', 521
  Primitive Groups, \indexit{413}
  `PrimitiveGroupsIterator', 521
  `PrimitiveIdentification', 522
  `PrimitiveIndexIrreducibleSolvableGroup', 523
  Primitive Permutation Groups, \indexit{520}
  `PrimitivePolynomial', 669
  `PrimitiveRoot', 580
  `PrimitiveRootMod', 138
  primitive root modulo an integer, 138
  Primitive Roots and Discrete Logarithms, \indexit{137}
  Primitivity of Characters, \indexit{815}
  `Print', 65
  `PrintAmbiguity', 806
  `PrintArray', 225
  `PrintCharacterTable', 741
  `PrintFactorsInt', 134
  `PrintFormattingStatus', 102
  Printing Character Tables, \indexit{738}
  Printing Class Functions, \indexit{764}
  Printing Presentations, \indexit{482}
  Printing Tables of Marks, \indexit{697}
  `PrintObj', 66
    \sub for character tables, 738, 764
    \sub for tables of marks, 697
  `PrintTo', 95
    \sub for streams, 101
  `ProbabilityShapes', 670
  problems, 827
  Problems on Particular Systems, \indexit{829}
  procedure call, 50
  Procedure Calls, \indexit{50}
  procedure call with arguments, 50
  `Process', 108
  Process, \indexit{108}
  `PROD_GF2MAT_GF2MAT_ADVANCED', 235
  `PROD_GF2MAT_GF2MAT_SIMPLE', 235
  `Product', 201
  product, of words, 331
    \sub rational functions, 662
  `ProductCoeffs', 217
  `ProductSpace', 615
  `ProductX', 203
  `ProfileFunctions', 82
  `ProfileGlobalFunctions', 82
  `ProfileMethods', 82
  `ProfileOperations', 81
  `ProfileOperationsAndMethods', 82
  `PROFILETHRESHOLD', 82
  Profiling, \indexit{81}
  `ProjectedInducedPcgs', 439
  `ProjectedPcElement', 439
  `Projection', 302
    \sub example for direct products, 499
    \sub example for semidirect products, 501
    \sub example for subdirect products, 501
    \sub example for wreath products, 502
    \sub for group products, 503
  `ProjectionMap', 802
  projections, find all, 389
  `ProjectiveActionHomomorphismMatrixGroup', 426
  `ProjectiveActionOnFullSpace', 426
  `ProjectiveGeneralLinearGroup', 509
  `ProjectiveGeneralUnitaryGroup', 509
  `ProjectiveOrder', 234
  `ProjectiveSpecialLinearGroup', 509
  `ProjectiveSpecialUnitaryGroup', 509
  `ProjectiveSymplecticGroup', 509
  prompt, 64
    \sub partial, 64
  Properties, \indexit{124}
  Properties and Attributes for Lists, \indexit{190}
  Properties and Attributes of (General) Mappings, \indexit{302}
  Properties and Attributes of Binary Relations, \indexit{311}
  Properties and Attributes of Matrices, \indexit{222}
  Properties and Attributes of Rational Functions, \indexit{663}
  Properties and basic functionality, \indexit{278}
  Properties of a Lie Algebra, \indexit{636}
  Properties of rewriting systems, \indexit{342}
  Properties of Rings, \indexit{560}
  Properties of Tables of Marks, \indexit{703}
  `PRump', 360
  `PseudoRandom', 274
  `PSL', 509
  `PSP', 509
  `PSp', 509
  `PSU', 509
  `PthPowerImage', 642
  `PthPowerImages', 642
  Pure p-adic Numbers, \indexit{685}
  `PurePadicNumberFamily', 685
  `PushOptions', 88
\letter Q
  `Quadratic', 162
  quadratic residue, 139
  `QuaternionAlgebra', 610
  `QUIET', 841
  `QUIT', emergency quit, 73
  quit, in emergency, 73
  `quit', 67
  `QUITTING', 73
  `QuoInt', 129
  `Quotient', 556
  quotient, for finitely presented groups, 459
    \sub matrices, 221
    \sub matrix and matrix list, 222
    \sub matrix and scalar, 221
    \sub of free monoid, 545
    \sub of free semigroup, 543
    \sub of words, 331
    \sub rational functions, 662
    \sub scalar and matrix, 221
    \sub scalar and matrix list, 222
    \sub vector and matrix, 221
  `QuotientFromSCTable', 609
  Quotient Methods, \indexit{472}
  `QuotientMod', 565
  `QuotientPolynomialsExtRep', 681
  `QuotientRemainder', 564
  Quotients, \indexit{535}
  Quotients and Remainders, \indexit{129}
  `QuotientSemigroupCongruence', 535
  `QuotientSemigroupHomomorphism', 535
  `QuotientSemigroupPreimage', 535
  `QuotRemLaurpols', 671
\letter R
  $r_N$, 160
  `RadicalGroup', 359
  `RadicalOfAlgebra', 618
  `Random', 273
    \sub for integers, 129
    \sub for rationals, 144
  `RandomBinaryRelationOnPoints', 313
  random element, of a list or collection, 273
  Random Elements, \indexit{273}
  `RandomInvertibleMat', 226
  `RandomIsomorphismTest', 457
  Random Isomorphism Testing, \indexit{457}
  Randomized Methods for Permutation Groups, \indexit{415}
  `RandomList', 274
  `RandomMat', 226
  Random Matrices, \indexit{226}
  `RandomPrimitivePolynomial', 582
  random seed, 274
  `RandomTransformation', 548
  `RandomUnimodularMat', 226
  `Range', 303
  range, 203
  Ranges, \indexit{203}
  `RankAction', 402
  `RankFilter', 117
  `RankMat', 226
  `RankOfTransformation', 549
  `RankPGroup', 364
  `Rat', 144
    \sub for strings, 254
  `RationalClass', 356
  `RationalClasses', 357
  `RationalFunctionByExtRep', 680
  `Rational\-Function\-By\-Ext\-Rep\-With\-Cancellation', 682
  Rational Function Families, \indexit{678}
  `RationalFunctionsFamily', 678
  `RationalizedMat', 163
  `Rationals', 143
  `RClassOfHClass', 536
  `Read', 94
    \sub for streams, 99
  `ReadAll', 100
  `ReadAllLine', 106
  `ReadAsFunction', 94
    \sub for streams, 99
  `ReadByte', 99
  read eval print loop, 64
  `ReadLine', 99
  `ReadPackage', 837
  `ReadPkg', 840
  `ReadTest', 84
    \sub for streams, 99
  `RealClasses', 730
  `RealizableBrauerCharacters', 790
  `RecNames', 258
  Recognizing Characters, \indexit{250}
  record, component access, 259
    \sub component assignment, 259
    \sub component variable, 259
    \sub component variable assignment, 260
  Record Access Operations, \indexit{263}
  Record Assignment, \indexit{259}
  record assignment, operation, 263
  record boundness test, operation, 263
  record component, operation, 263
  record unbind, operation, 263
  Recovery from NoMethodFound-Errors, \indexit{76}
  recursion, 55
  redisplay a help section, 23
  redisplay with next help viewer, 23
  `ReduceCoeffs', 217
  `ReduceCoeffsMod', 217
  `ReducedAdditiveInverse', 341
  `ReducedCharacters', 774
  `ReducedClassFunctions', 773
  `ReducedComm', 341
  `ReducedConfluentRewritingSystem', 546
  `ReducedConjugate', 341
  `ReducedDifference', 341
  `ReducedForm', 340
  `ReducedGroebnerBasis', 677
  `ReducedInverse', 341
  `ReducedLeftQuotient', 341
  `ReducedOne', 341
  `ReducedPcElement', 434
  `ReducedPower', 341
  `ReducedProduct', 341
  `ReducedQuotient', 341
  `ReducedScalarProduct', 341
  `ReducedSum', 341
  `ReducedZero', 341
  `ReduceRules', 341
  `ReduceStabChain', 421
  Reducing Virtual Characters, \indexit{773}
  `Ree', 506
  `ReeGroup', 506
  `ReesCongruenceOfSemigroupIdeal', 534
  `ReesMatrixSemigroup', 537
  `ReesMatrixSemigroupElement', 538
  Rees Matrix Semigroups, \indexit{537}
  `ReesZeroMatrixSemigroup', 537
  `ReesZeroMatrixSemigroupElement', 538
  `ReesZeroMatrixSemigroupElementIsZero', 538
  `RefinedPcGroup', 452
  `ReflectionMat', 225
  `ReflexiveClosureBinaryRelation', 313
  reflexive relation, 311
  regular, 402
  regular action, 399
  `RegularActionHomomorphism', 400
  `RegularModule', 744
  relations, 300
  Relations Between Domains, \indexit{294}
  `RelationsOfFpSemigroup', 544
  `RelativeBasis', 594
  `RelativeBasisNC', 594
  relatively prime, 48
  `RelativeOrderOfPcElement', 434
  `RelativeOrders', of a pcgs, 433
  Relators in a Presentation, \indexit{482}
  `RelatorsOfFpGroup', 460
  remainder, operation, 293
  remainder of a quotient, 129
  `RemInt', 129
  `Remove', 175
  remove, an element from a set, 194
  `RemoveFile', 96
  `RemoveOuterCoeffs', 215
  `RemoveRelator', 484
  `RemoveSet', 194
  `RemoveStabChain', 421
  Repeat, \indexit{52}
  `repeat' loop, 52
  `ReplacedString', 252
  Representation, \indexit{120}
  representation, as a sum of two squares, 142
  Representations for Associative Words, \indexit{333}
  Representations for Group Homomorphisms, \indexit{391}
  Representations given by modules, \indexit{744}
  Representations of Algebras, \indexit{623}
  `RepresentationsOfObject', 121
  `Representative', 270
  representative, of a list or collection, 271
  `RepresentativeAction', 398
  `RepresentativeLinearOperation', 623
  `RepresentativeOperation', 840
  `RepresentativesContainedRightCosets', 354
  `RepresentativesFusions', 800
  `RepresentativeSmallest', 271
  `RepresentativesMinimalBlocks', 403
  `RepresentativesPerfectSubgroups', 372
  `RepresentativesPowerMaps', 795
  `RepresentativesSimpleSubgroups', 372
  `RepresentativeTom', 711
  `RepresentativeTomByGenerators', 711
  `RepresentativeTomByGeneratorsNC', 711
  `RequirePackage', 840
  `Reread', 96
  `REREADING', 96
  `RereadPackage', 837
  `RereadPkg', 840
  `ResetOptionsStack', 88
  residue, quadratic, 139
  Residue Class Rings, \indexit{134}
  `RespectsAddition', 308
  `RespectsAdditiveInverses', 308
  `RespectsInverses', 307
  `RespectsMultiplication', 307
  `RespectsOne', 307
  `RespectsScalarMultiplication', 308
  `RespectsZero', 308
  `RestoreStateRandom', 273
  Restricted and Induced Class Functions, \indexit{771}
  `RestrictedClassFunction', 772
  `RestrictedClassFunctions', 772
  Restricted Lie algebras, \indexit{641}
  `RestrictedMapping', 302
  `RestrictedPartitions', 152
  `RestrictedPerm', 410
  `RestrictedTransformation', 549
  `Resultant', 667
  `ResultOfStraightLineProgram', 336
  Return, \indexit{58}
  `return', 68
    \sub no value, 58
    \sub with value, 58
  `ReturnFail', 63
  `ReturnFalse', 63
  return from break loop, 68
  `ReturnTrue', 63
  `Reversed', 196
  `RewindStream', 101
  `RewriteWord', 466
  Rewriting in Groups and Monoids, \indexit{342}
  Rewriting Systems and the Knuth-Bendix Procedure, \indexit{546}
  `RightActingAlgebra', 626
  `RightActingRingOfIdeal', 559
  `RightAlgebraModule', 624
  `RightAlgebraModuleByGenerators', 624
  `RightCoset', 352
  `RightCosets', 353
  right cosets, 352
  `RightCosetsNC', 353
  `RightDerivations', 633
  `RightIdeal', 557
  `RightIdealByGenerators', 558
  `RightIdealNC', 558
  `RightModuleByHomomorphismToMatAlg', 627
  `RightShiftRowVector', 215
  `RightTransversal', 353
  `Ring', 555
  `RingByGenerators', 556
  Ring Homomorphisms, \indexit{309}
  Rings With One, \indexit{559}
  `RingWithOne', 559
  `RingWithOneByGenerators', 560
  `RNamObj', 263
  root, of 1 modulo an integer, 140
    \sub of an integer, 128
    \sub of an integer, smallest, 128
    \sub of an integer modulo another, 139
  `RootInt', 128
  `RootMod', 139
  `RootOfDefiningPolynomial', 573
  `RootsMod', 139
  Roots Modulo Integers, \indexit{138}
  roots of unity, 155
  `RootsOfUPol', 666
  `RootsUnityMod', 140
  `RootSystem', 638
  `RoundCyc', 157
  Row and Matrix Spaces, \indexit{598}
  `RowIndexOfReesMatrixSemigroupElement', 538
  `Row\-Index\-Of\-Rees\-Zero\-Matrix\-Semigroup\-Element', 538
  row spaces, 598
  Row Vectors over Finite Fields, \indexit{213}
  `Rules', 340
  Running GAP under MacOS, \indexit{31}
  `Runtime', 81
  `Runtimes', 81
\letter S
  $s_N$, 160
  `SameBlock', 733
  `SandwichMatrixOfReesMatrixSemigroup', 538
  `SandwichMatrixOfReesZeroMatrixSemigroup', 538
  save, 37
  `SaveOnExitFile', 73
  `SaveWorkspace', 37
  Saving and Loading a Workspace, \indexit{37}
  Saving a Pc Group, \indexit{453}
  saving on exit, 73
  `ScalarProduct', for characters, 768
  Schreier, 479
  Schreier-Sims, random, 415
  `SchurCover', 378
  Schur Covers and Multipliers, \indexit{378}
  Schur multiplier, 378
  scope, 43
  `ScriptFromString', 708
  Searching for Homomorphisms, \indexit{389}
  `SecHMSM', 256
  secondary subgroup generators, 494
  `SecondsDMYhms', 256
  `SeekPositionStream', 101
  Selecting a Different MeatAxe, \indexit{689}
  Selection Functions, \indexit{511}
  `SemidirectProduct', 500
  Semidirect Products, \indexit{500}
  `SemiEchelonBasis', 600
  `SemiEchelonBasisNC', 600
  `SemiEchelonMat', 228
  `SemiEchelonMatDestructive', 229
  `SemiEchelonMats', 229
  `SemiEchelonMatsDestructive', 229
  `SemiEchelonMatTransformation', 229
  `Semigroup', 532
  semigroup, 532
  `SemigroupByGenerators', 532
  `SemigroupByMultiplicationTable', 533
  `SemigroupIdealByGenerators', 534
  `SemigroupOfRewritingSystem', 547
  semiregular, 402
  Semisimple Lie Algebras and Root Systems, \indexit{637}
  `SemiSimpleType', 637
  sequence, Bernoulli, 146
    \sub Fibonacci, 153
    \sub Lucas, 154
  Series of Ideals, \indexit{635}
  `Set', 267
  `SetAssertionLevel', 80
  `SetCommutator', 451
  `SetConjugate', 451
  `SetCrystGroupDefaultAction', 430
  set difference, of collections, 272
  `SetEntrySCTable', 608
  `SetGasmanMessageStatus', 86
  `SetHelpViewer', 24
  `SetIndeterminateName', 661
  `SetInfoLevel', 79
  `SetName', 115
  Set Operations via Boolean Lists, \indexit{208}
  `SetParent', 287
  `SetPower', 451
  `SetPrintFormattingStatus', 102
  `SetRecursionTrapInterval', 85
  `SetReducedMultiplication', 460
  Sets, \indexit{111}
  sets, 170, 193
  Sets of Subgroups, \indexit{369}
  set stabilizer, 397
  `Setter', 122
  setter, 122
  Setter and Tester for Attributes, \indexit{122}
  `SetX', 203
  `ShallowCopy', 114
    \sub for lists, 178
  `ShiftedCoeffs', 217
  `ShiftedPadicNumber', 685
  Shifting and Trimming Coefficient Lists, \indexit{215}
  `ShortestVectors', 244
  `ShortLexOrdering', 280
  short vectors spanning a lattice, 242, 774
  `ShowArgument', 76
  `ShowArguments', 76
  `ShowDetails', 76
  `ShowImpliedFilters', 118
  `ShowMethods', 77
  `ShowOtherMethods', 77
  `ShrinkCoeffs', 218
  `ShrinkRowVector', 215
  `SiftedPcElement', 434
  `SiftedPermutation', 420
  `SiftedVector', 601
  `Sigma', 140
  sign, of an integer, 127
  Sign and Cycle Structure, \indexit{409}
  `SignInt', 127
  `SignPartition', 152
  `SignPerm', 409
  `SimpleLieAlgebra', 633
  `SimpleSystem', 638
  `SimplifiedFpGroup', 478
  SimplifiedFpGroup, \indexit{478}
  `SimplifyPresentation', 485
  `SimsNo', 522
  `SimultaneousEigenvalues', 234
  `SingleCollector', 451
  singlequote character, 248
  singlequotes, 246
  `SINT_CHAR', 254
  `Size', 270
    \sub for character tables, 727
    \sub for groups with pcgs, 446
  size, of a list or collection, 270
  `SizeBlist', 208
  `SizeConsiderFunction', 374
  `SizeNumbersPerfectGroups', 517
  `SizeOfFieldOfDefinition', 790
  `SizesCentralizers', 728
  `SizesConjugacyClasses', 728
  `SizeScreen', 75
  SizeScreen, \indexit{75}
  `SizesPerfectGroups', 516
  `SizeStabChain', 419
  `SL', 507
  smaller, associative words, 330
    \sub elements of finitely presented groups, 460
    \sub nonassociative words, 324
    \sub pcwords, 449
    \sub rational functions, 663
  `SmallerDegreePermutationRepresentation', 412
  smaller or equal, 47
  smaller test, 47
  `SmallestGeneratorPerm', 408
  `SmallestMovedPoint', 408
  `SmallestRootInt', 128
  `SmallGeneratingSet', 375
  `SmallGroup', 514
  Small Groups, \indexit{513}
  `SmallGroupsInformation', 515
  Smash MeatAxe Flags, \indexit{693}
  smith normal form, 841
  `SmithNormalFormIntegerMat', 239
  `SmithNormalFormIntegerMatTransforms', 239
  `SMTX.AbsoluteIrreducibilityTest', 692
  `SMTX.AlgEl', 693
  `SMTX.AlgElCharPol', 693
  `SMTX.AlgElCharPolFac', 693
  `SMTX.AlgElMat', 693
  `SMTX.AlgElNullspaceDimension', 693
  `SMTX.AlgElNullspaceVec', 693
  `SMTX.CentMat', 693
  `SMTX.CentMatMinPoly', 693
  `SMTX.CompleteBasis', 692
  `SMTX.Getter', 692
  `SMTX.GoodElementGModule', 692
  `SMTX.IrreducibilityTest', 692
  `SMTX.MatrixSum', 692
  `SMTX.MinimalSubGModule', 692
  `SMTX.MinimalSubGModules', 692
  `SMTX.RandomIrreducibleSubGModule', 692
  `SMTX.Setter', 692
  `SMTX.SortHomGModule', 692
  `SMTX.Subbasis', 693
  `SO', 508
  `Socle', 360
  `SocleTypePrimitiveGroup', 413
  `SolutionIntMat', 237
  `SolutionMat', 227
  `SolutionMatDestructive', 227
  `SolutionNullspaceIntMat', 237
  Some Remarks about Character Theory in GAP, \indexit{716}
  Some Special Algebras, \indexit{610}
  `Sort', 192
  `SortedCharacters', 751
  `SortedCharacterTable', 752
  Sorted Character Tables, \indexit{751}
  `SortedList', 267
  sorted list, 191
  Sorted Lists and Sets, \indexit{193}
  sorted lists as collections, 265
  `SortedSparseActionHomomorphism', 399
  `SortedTom', 698
  `Sortex', 192
  Sorting Lists, \indexit{192}
  `SortingPerm', 193
  Sorting Tables of Marks, \indexit{698}
  `SortParallel', 192
  `Source', 303
  `SourceOfIsoclinicTable', 750
  `SP', 508
  `Sp', 508
  space, 41
  `SparseActionHomomorphism', 399
  `SparseCartanMatrix', 639
  Special Characters, \indexit{248}
  special character sequences, 248
  Special Filenames, \indexit{93}
  Special Generating Sets, \indexit{375}
  `SpecialLinearGroup', 507
  Special Multiplication Algorithms for Matrices over GF(2), \indexit{235}
  `SpecialOrthogonalGroup', 508
  Special Pcgs, \indexit{443}
  `SpecialPcgs', attribute, 443
  `SpecialUnitaryGroup', 508
  Specific and Parametrized Subgroups, \indexit{358}
  Specific Methods for Subgroup Lattice Computations, \indexit{372}
  `SplitCharacters', 746
  `SplitExtension', 455
  `SplitExtensions', 456
  `SplitString', 251
  `SplittingField', 665
  `Sqrt', 293
  square root, of an integer, 128
  `SquareRoots', 321
  `SSortedList', 267
  `StabChain', 417
  `StabChainBaseStrongGenerators', 418
  `StabChainImmutable', 417
  `StabChainMutable', 417
  `StabChainOp', 417
  `StabChainOptions', 418
  `Stabilizer', 397
  Stabilizer Chain Records, \indexit{418}
  Stabilizer Chains, \indexit{414}
  `StabilizerOfExternalSet', 405
  `StabilizerPcgs', 446
  Stabilizers, \indexit{397}
  `StandardAssociate', 562
  `StandardGeneratorsFunctions', 708
  `StandardGeneratorsInfo', for groups, 707
    \sub for tables of marks, 712
  `StandardGeneratorsOfGroup', 709
  Standard Generators of Groups, \indexit{707}
  Standardization of coset tables, \indexit{465}
  `StandardizeTable', 465
  `StarCyc', 162
  Statements, \indexit{49}
  `StateRandom', 273
  `Stirling1', 146
  `Stirling2', 147
  Stirling number of the first kind, 146
  Stirling number of the second kind, 147
  `StoredGroebnerBasis', 678
  `StoreFusion', 798
  Storing Normal Subgroup Information, \indexit{756}
  `StraightLineProgElm', 339
  `StraightLineProgGens', 339
  `StraightLineProgram', 335
  Straight Line Program Elements, \indexit{339}
  `StraightLineProgramNC', 335
  Straight Line Programs, \indexit{335}
  `StraightLineProgramsTom', 710
  `StreamsFamily', 98
  `StretchImportantSLPElement', 339
  strictly sorted list, 191
  `String', 251
    \sub for cyclotomics, 157
  `StringDate', 256
  `StringOfResultOfStraightLineProgram', 337
  `StringPP', 251
  strings, equality of, 250
    \sub inequality of, 250
    \sub lexicographic ordering of, 250
  String Streams, \indexit{104}
  `StringTime', 256
  `StrongGeneratorsStabChain', 419
  `StronglyConnectedComponents', 313
  <Struct>, 284
  `<Struct>ByGenerators', 285
  `StructuralCopy', 114
    \sub for lists, 178
  structure constant, 737, 738
  `StructureConstantsTable', 596
  `StructureDescription', 350
  Structure Descriptions, \indexit{350}
  `<Struct>WithGenerators', 285
  `SU', 508
  `Subalgebra', 611
  `SubAlgebraModule', 627
  `SubalgebraNC', 611
  Subalgebras, \indexit{611}
  `SubalgebraWithOne', 611
  `SubalgebraWithOneNC', 612
  `SubdirectProduct', 501
  Subdirect Products, \indexit{501}
  `SubdirectProducts', 502
  subdomains, 288
  `Subfield', 573
  `SubfieldNC', 573
  `Subfields', 573
  Subfields of Fields, \indexit{573}
  `Subgroup', 347
  `SubgroupByPcgs', 437
  `SubgroupByProperty', 348
  subgroup fusions, 796
  subgroup generators tree, 494
  Subgroup Lattice, \indexit{370}
  `SubgroupNC', 347
  `SubgroupOfWholeGroupByCosetTable', 466
  `SubgroupOfWholeGroupByQuotientSubgroup', 471
  Subgroup Presentations, \indexit{479}
  `SubgroupProperty', 422
  Subgroups, \indexit{347}
  subgroups, polyhedral, 737
  Subgroups characterized by prime powers, \indexit{361}
  Subgroup Series, \indexit{365}
  `SubgroupShell', 348
  Subgroups of Polycyclic Groups - Canonical Pcgs, \indexit{437}
  Subgroups of Polycyclic Groups - Induced Pcgs, \indexit{436}
  `SubgroupsSolvableGroup', 373
  sublist, 172
    \sub access, 172
    \sub assignment, 174
    \sub operation, 173
  sublist assignment, operation, 175
  `Submagma', 317
  `SubmagmaNC', 317
  `SubmagmaWithInverses', 317
  `SubmagmaWithInversesNC', 317
  `SubmagmaWithOne', 317
  `SubmagmaWithOneNC', 317
  `Submodule', 568
  `SubmoduleNC', 568
  Submodules, \indexit{568}
  `Submonoid', 539
  `SubmonoidNC', 539
  `SubnearAdditiveGroup', 553
  `SubnearAdditiveGroupNC', 553
  `SubnearAdditiveMagma', 553
  `SubnearAdditiveMagmaNC', 553
  `SubnearAdditiveMagmaWithZero', 553
  `SubnearAdditiveMagmaWithZeroNC', 553
  `SubnormalSeries', 365
  `Subring', 556
  `SubringNC', 556
  `SubringWithOne', 560
  `SubringWithOneNC', 560
  Subroutines for the Construction of Class Fusions, \indexit{811}
  Subroutines for the Construction of Power Maps, \indexit{809}
  `Subsemigroup', 532
  `SubsemigroupNC', 532
  subsets, 147
  subset test, for collections, 271
  `Subspace', 590
  `SubspaceNC', 590
  `Subspaces', 592
  `SubstitutedWord', 332
  `SubsTom', 700
  `Sub<struct>', 288
  `Sub<struct>NC', 288
  `SubSyllables', 333
  subtract, a set from another, 195
  `SubtractBlist', 209
  subtraction, 48
    \sub matrices, 220
    \sub matrix and scalar, 220
    \sub rational functions, 662
    \sub scalar and matrix, 220
    \sub scalar and matrix list, 222
    \sub scalar and vector, 212
    \sub vector and scalar, 212
    \sub vectors, 212
  `SubtractSet', 195
  `Subword', 331
  `Successors', 312
  Suitability for Compilation, \indexit{35}
  `Sum', 201
  Sum and Intersection of Pcgs, \indexit{442}
  `SumFactorizationFunctionPcgs', 442
  `SumIntersectionMat', 230
  `SumX', 203
  `SupersolvableResiduum', 360
  `support', email address, 828
  `SupportedCharacterTableInfo', 720
  `SurjectiveActionHomomorphismAttr', 406
  `SuzukiGroup', 506
  `SylowComplement', 360
  `SylowSubgroup', 360
  Sylow Subgroups and Hall Subgroups, \indexit{360}
  `SylowSystem', 361
  Symbols, \indexit{40}
  Symmetric and Alternating Groups, \indexit{412}
  `SymmetricClosureBinaryRelation', 313
  `SymmetricGroup', 506
  symmetric group, powermap, 153
  `SymmetricParentGroup', 413
  `SymmetricParts', 780
  `SymmetricPowerOfAlgebraModule', 652
  symmetric relation, 312
  `Symmetrizations', 779
  symmetrizations, orthogonal, 780, 781
    \sub symplectic, 781
  Symmetrizations of Class Functions, \indexit{779}
  `SymplecticComponents', 781
  `SymplecticGroup', 508
  syntax errors, 64
  system getter, 121
  system setter, 121
  `Sz', 506
\letter T
  $t_N$, 160
  `TableAutomorphisms', 754
  table automorphisms, 800, 812
  table of chapters for help books, 23
  `TableOfMarks', 695
  `TableOfMarksByLattice', 696
  `TableOfMarksComponents', 699
  `TableOfMarksCyclic', 714
  `TableOfMarksDihedral', 714
  `TableOfMarksFamily', 699
  `TableOfMarksFrobenius', 714
  Table of Marks Objects in GAP, \indexit{695}
  table of sections for help books, 23
  tables, 716, 718
  tabulator, 41
  `Tau', 140
  Technical Details about Tables of Marks, \indexit{699}
  Technical Details about the Implementation of Magma Rings, \indexit{658}
  Technical Matters Concerning General Mappings, \indexit{309}
  `TemporaryGlobalVarName', 46
  `Tensored', 771
  `TensorProductGModule ', 688
  `TensorProductOfAlgebraModules', 651
  Tensor Products and Exterior and Symmetric Powers, \indexit{651}
  test, for a primitive root, 138
    \sub for a rational, 143
    \sub for records, 258
    \sub for set equality, 194
  `TestConsistencyMaps', 805
  `Tester', 122
  tester, 122
  Test Files, \indexit{84}
  `TestHomogeneous', 815
  `TestInducedFromNormalSubgroup', 817
  Testing Finiteness of Finitely Presented Groups, \indexit{475}
  Testing for the System Architecture, \indexit{34}
  Testing Monomiality, \indexit{817}
  `TestJacobi', 608
  `TestMonomial', 817
  `TestMonomialQuick', 818
  `TestMonomialUseLattice', 818
  Test of the installation, \indexit{824}
  `TestPackageAvailability', 838
  `TestPerm1', 787
  `TestPerm2', 787
  `TestPerm3', 787
  `TestPerm4', 787
  `TestPerm5', 787
  `TestQuasiPrimitive', 816
  `TestRelativelySM', 819
  Tests for Actions, \indexit{402}
  Tests for the Availability of Methods, \indexit{378}
  `TestSubnormallyMonomial', 819
  The .gaprc file, \indexit{33}
  The Adjoint Representation, \indexit{643}
  The Compiler, \indexit{35}
  The Defining Attributes of Rational Functions, \indexit{679}
  The Dixon-Schneider Algorithm, \indexit{744}
  The Documentation, \indexit{826}
  The External Representation for Associative Words, \indexit{335}
  The family pcgs, \indexit{449}
  The Interface between Character Tables and Groups, \indexit{722}
  The Interface between Tables of Marks and Character Tables, \indexit{712}
  The Library of Tables of Marks, \indexit{715}
  `then', 51
  The Natural Action, \indexit{411}
  The Pager Command, \indexit{25}
  The Permutation Image of an Action, \indexit{398}
  The Representations of Rational Functions, \indexit{679}
  The Smash MeatAxe, \indexit{692}
  The Syntax in BNF, \indexit{59}
  `ThreeGroup' library, 514
  Tietze Options, \indexit{497}
  Tietze Transformations, \indexit{484}
  Tietze Transformations that introduce new Generators, \indexit{489}
  `TietzeWordAbstractWord', 482
  `time', 81
  Timing, \indexit{81}
  Todd-Coxeter Procedure, \indexit{547}
  `Trace', 223
    \sub for field elements, 575
    \sub of a matrix, 223
  `TracedCosetFpGroup', 463
  `TraceImmediateMethods', 78
  `TraceMat', 223
  `TraceMethods', 78
  `TracePolynomial', 574
  Tracing generator images through Tietze transformations, \indexit{492}
  Tracing Methods, \indexit{78}
  `TransferDiagram', 805
  `Transformation', 548
  `TransformationData', 548
  `TransformationFamily', 548
  `TransformationNC', 548
  `TransformationRelation', 550
  `TransformationType', 548
  `TransformingPermutations', 754
  `TransformingPermutationsCharacterTables', 755
  transitive, 402
  `TransitiveClosureBinaryRelation', 313
  `TransitiveGroup', 512
  `TransitiveIdentification', 512
  Transitive Permutation Groups, \indexit{512}
  transitive relation, 312
  `Transitivity', for characters, 770
    \sub for class functions, 770
    \sub for group actions, 402
  `TranslatorSubalgebra', 630
  transporter, 398
  `TransposedMat', 224
  `TransposedMatAttr', 224
  `TransposedMatDestructive', 225
  `TransposedMatImmutable', 224
  `TransposedMatMutable', 224
  `TransposedMatOp', 224
  `TransposedMatrixGroup', 425
  Transversals, \indexit{353}
  Triangular Matrices, \indexit{231}
  `TriangulizedIntegerMat', 238
  `TriangulizedIntegerMatTransform', 238
  `TriangulizedNullspaceMat', 226
  `TriangulizedNullspaceMatDestructive', 226
  `TriangulizeIntegerMat', 238
  `TriangulizeMat', 226
  `TrivialCharacter', 766
  `TrivialGroup', 504
  `TrivialIterator', 276
  `TrivialSubalgebra', 612
  `TrivialSubgroup', 358
  `TrivialSubmagmaWithOne', 321
  `TrivialSubmodule', 568
  `TrivialSubmonoid', 539
  `TrivialSubnearAdditiveMagmaWithZero', 553
  `TrivialSubspace', 591
  `TryCosetTableInWholeGroup', 466
  `TryGcdCancelExtRepPolynomials', 682
  `Tuples', 149
  tuple stabilizer, 397
  `TwoClosure', 422
  `TwoCoboundaries', 454
  `TwoCocycles', 454
  `TwoCohomology', 454
  `TwoGroup' library, 514
  `TwoSidedIdeal', 557
  `TwoSidedIdealByGenerators', 558
  `TwoSidedIdealNC', 558
  `TwoSquares', 142
  type, boolean, 167
    \sub cyclotomic, 155
    \sub records, 258
    \sub strings, 246
  `TypeObj', 125
  `TypeOfDefaultGeneralMapping', 310
  Types, \indexit{125}
  `TzEliminate', 487
  `TzFindCyclicJoins', 488
  `TzGo', 485
  `TzGoGo', 486
  `TzImagesOldGens', 493
  `TzInitGeneratorImages', 492
  `TzNewGenerator', 484
  `TzOptions', 497
  `TzPreImagesNewGens', 493
  `TzPrint', 483
  `TzPrintGeneratorImages', 493
  `TzPrintGenerators', 482
  `TzPrintLengths', 483
  `TzPrintOptions', 498
  `TzPrintPairs', 483
  `TzPrintPresentation', 483
  `TzPrintRelators', 482
  `TzPrintStatus', 483
  `TzSearch', 487
  `TzSearchEqual', 488
  `TzSort', 476
  `TzSubstitute', 489
  `TzSubstituteCyclicJoins', 492
\letter U
  $u_N$, 160
  `UglyVector', 604
  `Unbind', 44
    \sub for lists, 176
  `UnbindGlobal', 45
  `UnderlyingCharacteristic', 729
  `UnderlyingCharacterTable', 760
  `UnderlyingElement', fp group elements, 461
    \sub fp semigroup elements, 545
  `Underlying\-Element\-Of\-Rees\-Matrix\-Semigroup\-Element', 538
  `Underlying\-Element\-Of\-Rees\-Zero\-Matrix\-Semigroup\-Element', 538
  `UnderlyingExternalSet', 406
  `UnderlyingFamily', 632
  `UnderlyingGeneralMapping', 303
  `UnderlyingGroup', for character tables, 722
    \sub for tables of marks, 701
  `UnderlyingLeftModule', 594
  `UnderlyingLieAlgebra', 638
  `UnderlyingMagma', 655
  `UnderlyingRelation', 303
  `UnInstallCharReadHookFunc', 107
  `Union', 272
  union, of collections, 272
    \sub of sets, 194
  `Union2', 272
  `UnionBlist', 208
  `Unique', 196
  `UniteBlist', 209
  `UniteBlistList', 209
  `UniteSet', 194
  `Units', 561
  Units and Factorizations, \indexit{561}
  `UnivariatenessTestRationalFunction', 666
  `UnivariatePolynomial', 665
  `UnivariatePolynomialByCoefficients', 665
  `UnivariatePolynomialRing', 673
  Univariate Polynomial Rings, \indexit{673}
  Univariate Polynomials, \indexit{665}
  `Univariate\-Rational\-Function\-By\-Coefficients', 671
  Univariate Rational Functions, \indexit{671}
  `UniversalEnvelopingAlgebra', 644
  Universal Enveloping Algebras, \indexit{644}
  UNIX, features, 27
    \sub options, 27
  `UNIXSelect', 98
  `Unknown', 165
  `UnloadSmallGroupsData', 515
  `UnorderedTuples', 148
  Unpacking, \indexit{822}
  `UnprofileFunctions', 82
  `UnprofileMethods', 82
  `until', 52
  `UntraceMethods', 78
  `UpdateMap', 803
  `UpEnv', 71
  `UpperCentralSeriesOfGroup', 367
  `UpperSubdiagonal', 231
  `UseBasis', 570
  `UseFactorRelation', 294
  Useful Categories for all Elements of a Family, \indexit{298}
  Useful Categories of Elements, \indexit{296}
  `UseIsomorphismRelation', 294
  User Streams, \indexit{104}
  `UseSubsetRelation', 294
  utilities for editing GAP files, 75
\letter V
  $v_N$, 160
  `Valuation', 685
  `Value', 667
  `ValueCochain', 647
  `ValueGlobal', 45
  `ValueMolienSeries', 783
  `ValueOption', 89
  `ValuePol', 217
  `ValuesOfClassFunction', 760
  Variable Access in a Break Loop, \indexit{71}
  Variables, \indexit{43}
  Vectors as coefficients of polynomials, \indexit{216}
  `VectorSpace', 590
  `Vector\-Space\-By\-Pcgs\-Of\-Elementary\-Abelian\-Group', 445
  Vector Space Homomorphisms, \indexit{601}
  Vector Spaces Handled By Nice Bases, \indexit{603}
  `vi', 75
  `View', 65
  View and Print, \indexit{65}
  `ViewObj', 66
    \sub for character tables, 738
    \sub for class functions, 764
    \sub for tables of marks, 697
  `vim', 75
  `VirtualCharacter', 765
  virtual character, 767
  virtual characters, 758
\letter W
  $w_N$, 160
  `WedgeGModule ', 688
  `WeekDay', 256
  `WeightLexOrdering', 280
  `WeightOfGenerators', 281
  `WeightsTom', 703
  `WeightVecFFE', 216
  `WeylGroup', 640
  `WeylOrbitIterator', 641
  `Where', 70
  While, \indexit{52}
  `while' loop, 52
  Whitespaces, \indexit{41}
  Why Class Functions?, \indexit{758}
  `WordAlp', 251
  words, in generators, 349
  Working with large degree permutation groups, \indexit{423}
  `WreathProduct', 502
  wreath product embedding, 503
  `WreathProductImprimitiveAction', 503
  `WreathProductOrdering', 282
  `WreathProductProductAction', 503
  Wreath Products, \indexit{502}
  `WriteAll', 101
  `WriteByte', 101
  `WriteLine', 101
\letter X
  $x_N$, 160
\letter Y
  $y_N$, 160
\letter Z
  `Z', 577
  `ZClassRepsQClass', 429
  `Zero', 290
  `ZeroAttr', 290
  `ZeroCoefficient', 656
  `ZeroCoefficientRatFun', 680
  `ZeroImmutable', 290
  `ZeroMapping', 302
  `ZeroMutable', 290
  `ZeroOp', 290
  `ZeroSameMutability', 290
  `ZeroSM', 290
  `ZippedProduct', 681
  `ZippedSum', 681
  `ZmodnZ', 135
  `ZmodnZObj', 135
  `ZmodpZ', 135
  `ZmodpZNC', 135
  `ZumbroichBase', 586
  `Zuppos', 372
