\letter {}
  (Near-)Additive Magma Categories, \indexit{546}
  (Near-)Additive Magma Generation, \indexit{547}
  `+', 47
  `-', 47
  `-A', 29
  `-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', 28
  `-m', 28
  `-n', 27
    \sub on Macintosh, 31
  `-o', 28
    \sub on Macintosh, 31
  `-q', 27
  `-r', 29
  `-x', 27
  `-y', 28
  `-z', 30
    \sub on Macintosh, 31
  `.gaprc', 33
  `/', 47
    \sub for character tables, 717
  `\*', 47
    \sub for character tables, 717
  `\\\char 39', 244
  `\\XYZ', 244
  `\\\"', 244
  `\\\\', 244
  `\\b', 244
  `\\c', 244
  `\\in', operation for testing membership, 268
  `\\n', 244
  `\\r', 244
  `{\accent 94 }', 47
    \sub for class functions, 755
  1-Cohomology, \indexit{370}
  2-Cohomology and Extensions, \indexit{448}
\letter A
  `AbelianGroup', 500
  `AbelianInvariants', for character tables, 720
    \sub for groups, 358
  Abelian Invariants for Subgroups, \indexit{468}
  `AbelianInvariantsMultiplier', 373
  `AbelianInvariantsNormalClosureFpGroup', 469
  `Abelian\-Invariants\-Normal\-Closure\-Fp\-Group\-Rrs', 469
  `AbelianInvariantsOfList', 236
  `AbelianInvariantsSubgroupFpGroup', 468
  `AbelianInvariantsSubgroupFpGroupMtc', 468
  `AbelianInvariantsSubgroupFpGroupRrs', 468
  `AbelianNumberField', 577
  abelian number field, 578
  abelian number fields, canonicalbasis, 580
  abelian number fields, Galois group, 581
  `AbelianSubfactorAction', 395
  About Group Actions, \indexit{387}
  `AbsInt', 126
  `AbsoluteIrreducibleModules', 736
  `AbsoluteValue', 155
  absolute value of an integer, 126
  `AbsolutIrreducibleModules', 736
  abstract word, 318
  `AbstractWordTietzeWord', 477
  accessing, list elements, 170
    \sub record elements, 254
  Accessing a Module, \indexit{682}
  Accessing Record Elements, \indexit{254}
  Accessing Subgroups via Tables of Marks, \indexit{703}
  `AClosestVectorCombinationsMatFFEVecFFE', 213
  `ActingAlgebra', 620
  `ActingDomain', 399
  Acting OnRight and OnLeft, \indexit{424}
  `Action', 394
  action, by conjugation, 388
    \sub on blocks, 388
    \sub on sets, 388
  `ActionHomomorphism', 393
  Action of a group on itself, \indexit{395}
  Action on Subfactors Defined by a Pcgs, \indexit{439}
  actions, 388
  Actions of Matrix Groups, \indexit{421}
  `ActorOfExternalSet', 401
  `Add', 173
  add, an element to a set, 191
  `AddCoeffs', 211
  `AddGenerator', 479
  `AddGenerators', 337
  `AddGeneratorsExtendSchreierTree', 416
  addition, 47
    \sub list and non-list, 181
    \sub matrices, 216
    \sub matrix and scalar, 216
    \sub operation, 289
    \sub rational functions, 656
    \sub scalar and matrix, 216
    \sub scalar and matrix list, 217
    \sub scalar and vector, 209
    \sub vector and scalar, 209
    \sub vectors, 208
  Additive Arithmetic for Lists, \indexit{180}
  `AdditiveInverse', 287
  `AdditiveInverseAttr', 287
  `AdditiveInverseImmutable', 287
  `AdditiveInverseMutable', 287
  `AdditiveInverseOp', 287
  `AdditiveInverseSameMutability', 287
  `AdditiveInverseSM', 287
  `AdditiveNeutralElement', 548
  `AddRelator', 479
  `AddRowVector', 211
  `AddRule', 337
  `AddRuleReduced', 337
  `AddSet', 191
  `AdjointAssociativeAlgebra', 637
  `AdjointBasis', 609
  `AdjointMatrix', 637
  `AdjointModule', 621
  Advanced Features of GAP, \indexit{29}
  Advanced List Manipulations, \indexit{199}
  Advanced Methods for Dixon-Schneider Calculations, \indexit{737}
  `AffineAction', 440
  `AffineActionLayer', 440
  `AffineOperation', 440
  `AffineOperationLayer', 440
  `Agemo', 356
  `Algebra', 600
  `AlgebraByStructureConstants', 603
  `AlgebraGeneralMappingByImages', 614
  `AlgebraHomomorphismByImages', 614
  `AlgebraHomomorphismByImagesNC', 614
  `AlgebraicExtension', 677
  `AlgebraWithOne', 600
  `AlgebraWithOneGeneralMappingByImages', 614
  `AlgebraWithOneHomomorphismByImages', 615
  `AlgebraWithOneHomomorphismByImagesNC', 615
  `AllBlocks', 398
  `AllIrreducibleSolvableGroups', 518
  `All<Library>Groups', 506
  `AllPrimitiveGroups', 506
  `AllSmallGroups', 509
  `AllTransitiveGroups', 506
  `Alpha', 806
  `AlternatingGroup', 500
  `and', 166
    \sub for filters, 116, 167
  An Example of Advanced Dixon-Schneider Calculations, \indexit{738}
  `ANFAutomorphism', 582
  `AntiSymmetricParts', 772
  antisymmetric relation, 308
  `Append', 173
  `AppendTo', 94
    \sub for streams, 100
  Apple, 822, 823
  `ApplicableMethod', 76
  ApplicableMethod, \indexit{76}
  `ApplicableMethodTypes', 76
  `Apply', 194
  `ApplySimpleReflection', 634
  `ApproximateSuborbitsStabilizerPermGroup', 415
  `ARCH_IS_MAC', 34
  `ARCH_IS_UNIX', 34
  `ARCH_IS_WINDOWS', 34
  `arg', special function argument, 45, 55
  Arithmetic for External Representations of Polynomials, \indexit{675}
  Arithmetic for Lists, \indexit{178}
  Arithmetic Operations for Class Functions, \indexit{753}
  Arithmetic Operations for Elements, \indexit{289}
  Arithmetic Operations for General Mappings, \indexit{301}
  Arithmetic Operators, \indexit{47}
  `Arrangements', 145
  arrow notation for functions, 56
  `AsAlgebra', 609
  `AsAlgebraWithOne', 610
  `AsBinaryRelationOnPoints', 309
  `AsBlockMatrix', 231
  `AscendingChain', 362
  `AsDivisionRing', 567
  `AsDuplicateFreeList', 193
  `AsField', 567
  `AsFreeLeftModule', 564
  `AsGroup', 342
  `AsGroupGeneralMappingByImages', 376
  `AsLeftIdeal', 554
  `AsLeftModule', 562
  `AsList', 264
  `AsMagma', 313
  `AsMonoid', 534
  `AsPolynomial', 658
  `AsRightIdeal', 554
  `AsRing', 551
  `AsSemigroup', 527
  `Assert', 79
  `AssertionLevel', 79
  Assertions, \indexit{79}
  `AsSet', 264
  `AssignGeneratorVariables', 325
  assignment, to a list, 171
    \sub to a record, 255
    \sub variable, 48
  Assignments, \indexit{48}
  `AssignNiceMonomorphismAutomorphismGroup', 383
  `AssociatedPartition', 150
  `AssociatedReesMatrixSemigroupOfDClass', 533
  `Associates', 557
  associativity, 47
  `AssocWordByLetterRep', 330
  `AsSortedList', 264
  `AsSSortedList', 264
  `As<Struct>', 281
  `AsSubalgebra', 610
  `AsSubalgebraWithOne', 610
  `AsSubgroup', 343
  `AsSubgroupOfWholeGroupByQuotient', 466
  `AsSubmagma', 313
  `AsSubmonoid', 534
  `AsSubsemigroup', 527
  `AsSubspace', 585
  `AsSub<struct>', 284
  `AsTransformation', 544
  `AsTransformationNC', 544
  `AsTwoSidedIdeal', 554
  `AsVectorSpace', 584
  at exit functions, 71
  ATLAS Irrationalities, \indexit{157}
  `AtlasIrrationality', 159
  atomic irrationalities, 157
  Attributes, \indexit{120}
  Attributes and Operations for Algebras, \indexit{608}
  Attributes and Properties for (Near-)Additive Magmas, \indexit{548}
  Attributes and Properties for Collections, \indexit{265}
  Attributes and Properties for Magmas, \indexit{315}
  Attributes and Properties for Matrix Groups, \indexit{420}
  Attributes and Properties of Character Tables, \indexit{718}
  Attributes and Properties of Elements, \indexit{285}
  Attributes of and Operations on Equivalence Relations, \indexit{310}
  Attributes of Tables of Marks, \indexit{693}
  `AttributeValueNotSet', 121
  `AugmentationIdeal', 649
  `AugmentedCosetTableInWholeGroup', 461
  `AugmentedCosetTableMtc', 461
  `AugmentedCosetTableRrs', 461
  Augmented Coset Tables and Rewriting, \indexit{461}
  automatic loading of gap packages, 828
  `AutomorphismDomain', 382
  `AutomorphismGroup', 382
    \sub for groups with pcgs, 441
  automorphism group, of number fields, 581
  Automorphisms and Equivalence of Character Tables, \indexit{745}
  `AutomorphismsOfTable', 721
\letter B
  $b_N$, 157
  backslash character, 244
  backspace character, 244
  `Backtrace', GAP3 name for `Where', 69
  Backtrack, \indexit{417}
  `BANNER', 833
  `BaseFixedSpace', 223
  `BaseIntersectionIntMats', 233
  `BaseIntMat', 233
  `BaseMat', 225
  `BaseMatDestructive', 225
  `BaseOfGroup', 414
  `BaseOrthogonalSpaceMat', 226
  Bases of Vector Spaces, \indexit{586}
  `BaseStabChain', 414
  `BaseSteinitzVectors', 226
  Basic Actions, \indexit{388}
  Basic Groups, \indexit{499}
  Basic Operations for Class Functions, \indexit{752}
  Basic Operations for Lists, \indexit{169}
  `BasicWreathProductOrdering', 277
  `Basis', 587
  `BasisNC', 587
  `BasisVectors', 588
  `Bell', 143
  `Bernoulli', 144
  `BestQuoInt', 128
  `BestSplittingMatrix', 738
  `BiAlgebraModule', 618
  `BiAlgebraModuleByGenerators', 618
  `BilinearFormMat', 632
  binary relation, 307
  `BinaryRelationByElements', 307
  `BinaryRelationOnPoints', 308
  `BinaryRelationOnPointsNC', 308
  Binary Relations on Points, \indexit{308}
  `BinaryRelationTransformation', 545
  `BindGlobal', 44
  `Binomial', 143
  blank, 39
  `BlistList', 204
  Block Matrices, \indexit{231}
  `BlockMatrix', 231
  `Blocks', 398
  `BlocksInfo', 726
  Block Systems, \indexit{398}
  `BlownUpMat', 228
  `BlownUpVector', 228
  `BlowUpIsomorphism', 421
  BNF, 57
  body, 54
  `BombieriNorm', 664
  Boolean Lists Representing Subsets, \indexit{204}
  bound, 41
  Brauer character, 759
  `BrauerCharacterValue', 782
  `BrauerTable', 712
  `BrauerTableOp', 712
  `BravaisGroup', 424
  `BravaisSubgroups', 424
  `BravaisSupergroups', 424
  Break, \indexit{53}
  break loop message, 68
  Break Loops, \indexit{66}
  `break' statement, 53
  browsing backwards, 22
  browsing backwards one chapter, 22
  browsing forward, 22
  browsing forward one chapter, 22
  browsing the next section browsed, 22
  browsing the previous section browsed, 22
  Browsing through the Sections, \indexit{22}
  bug reports, see If Things Go Wrong, 820
  Building new orderings, \indexit{273}
\letter C
  $c_N$, 157
  Calculating with Group Automorphisms, \indexit{383}
  Calendar Arithmetic, \indexit{251}
  `CallFuncList', 60
  Calling a function with a list argument that is interpreted as several arguments, \indexit{60}
  Cancellation Tests for Rational Functions, \indexit{675}
  `CanComputeIndex', 374
  `CanComputeIsSubset', 374
  `CanComputeSize', 373
  `CanComputeSizeAnySubgroup', 374
  candidates, for permutation characters, 775, 777
  `CanEasilyCompareElements', 288
  `CanEasilyCompareElementsFamily', 288
  `CanEasilyComputePcgs', 427
  `CanEasilySortElements', 288
  `CanEasilySortElementsFamily', 288
  `CanEasilyTestMembership', 373
  `CanonicalBasis', 587
  canonical basis, for matrix spaces, 594
    \sub for row spaces, 594
  `CanonicalGenerators', 632
  `CanonicalPcElement', 429
  `CanonicalPcgs', 432
  `CanonicalPcgsByGeneratorsWithImages', 434
  `Canonical\-Representative\-Determinator\-Of\-External\-Set', 401
  `CanonicalRepresentativeOfExternalSet', 400
  `CanonicalRightCosetElement', 347
  Carmichael's lambda function, 134
  carriage return character, 244
  `CartanMatrix', 632
  `CartanSubalgebra', 629
  `Cartesian', 195
  Categories, \indexit{117}
  Categories and Properties of Algebras, \indexit{607}
  Categories for Streams and the StreamsFamily, \indexit{96}
  Categories of Associative Words, \indexit{323}
  Categories of Matrices, \indexit{215}
  `CategoriesOfObject', 119
  Categories of Words and Nonassociative Words, \indexit{318}
  `CategoryCollections', 260
  `Center', 316
  center, 315
  `CentralCharacter', 762
  central character, 762
  `CentralIdempotentsOfAlgebra', 612
  centraliser, 315
  `Centralizer', 315
    \sub for groups with pcgs, 441
  `CentralizerInGLnZ', 424
  `CentralizerModulo', 363
  `CentralizerSizeLimitConsiderFunction', 442
  `CentralNormalSeriesByPcgs', 435
  `Centre', 316
    \sub for groups with pcgs, 441
  centre, of a character, 761
  `CentreOfCharacter', 761
  `CF', 577
  `ChangeStabChain', 416
  Changing Presentations, \indexit{478}
  Changing the Help Viewer, \indexit{23}
  Changing the Representation, \indexit{282}
  Changing the Structure, \indexit{281}
  `CHAR_INT', 249
  `CHAR_SINT', 250
  `Character', 757
  Character Conversion, \indexit{249}
  `CharacterDegrees', 718
  Character Degrees and Derived Length, \indexit{806}
  `Characteristic', 285
  characteristic, for class functions, 756
  `CharacteristicPolynomial', 227
  characteristic polynomial, for field elements, 569
  `CharacterNames', 722
  characters, 750
    \sub permutation, 775, 777
    \sub symmetrizations of, 771
  `CharacterTable', 712
  Character Table Categories, \indexit{713}
  `CharacterTableDirectProduct', 740
  `CharacterTableFactorGroup', 741
  `CharacterTableIsoclinic', 742
  character tables, 711
    \sub access to, 711
    \sub calculate, 711
    \sub infix operators, 717
    \sub of groups, 711
  `CharacterTableWithSortedCharacters', 743
  `CharacterTableWithSortedClasses', 743
  `CharacterTableWreathSymmetric', 742
  character value, of group element using powering operator, 755
  `CharsFamily', 245
  `CheckFixedPoints', 796
  `CheckForHandlingByNiceBasis', 599
  `CheckPermChar', 803
  `ChevalleyBasis', 631
  `ChiefNormalSeriesByPcgs', 436
  `ChiefSeries', 359
  `ChiefSeriesThrough', 359
  `ChiefSeriesUnderAction', 359
  `ChineseRem', 129
  Chinese remainder, 129
  `Chomp', 249
  `CIUnivPols', 655
  `ClassElementLattice', 365
  classes, real, 723
  `ClassesSolvableGroup', 441
  `ClassFunction', 757
  class function, 750
  class function objects, 750
  class functions, 793
    \sub as ring elements, 754
  `ClassFunctionSameType', 758
  Class Fusions between Character Tables, \indexit{788}
  Classical Groups, \indexit{501}
  `ClassMultiplicationCoefficient', for character tables, 730
  class multiplication coefficient, 730, 731
  `ClassNames', 722
  `ClassNamesTom', 694
  `ClassOrbit', 723
  `ClassPermutation', 744
  `ClassPositionsOfAgemo', 724
  `ClassPositionsOfCentre', for characters, 761
    \sub for character tables, 724
  `ClassPositionsOfDerivedSubgroup', 724
  `Class\-Positions\-Of\-Direct\-Product\-Decompositions', 724
  `ClassPositionsOfElementaryAbelianSeries', 724
  `ClassPositionsOfFittingSubgroup', 724
  `ClassPositionsOfKernel', 761
  `ClassPositionsOfLowerCentralSeries', 724
  `ClassPositionsOfMaximalNormalSubgroups', 724
  `ClassPositionsOfNormalClosure', 724
  `ClassPositionsOfNormalSubgroup', 748
  `ClassPositionsOfNormalSubgroups', 724
  `ClassPositionsOfSupersolvableResiduum', 724
  `ClassPositionsOfUpperCentralSeries', 724
  `ClassRoots', 723
  `ClassStructureCharTable', 730
  `ClassTypesTom', 694
  `CleanedTailPcElement', 429
  `ClearCacheStats', 82
  `ClearProfile', 81
  clone, an object, 113
  `CloseMutableBasis', 592
  `CloseStream', 97
  `ClosureGroup', 344
  `ClosureGroupAddElm', 345
  `ClosureGroupCompare', 345
  `ClosureGroupDefault', 345
  `ClosureGroupIntest', 345
  `ClosureLeftModule', 563
  `ClosureNearAdditiveGroup', 548
  Closure Operations and Other Constructors, \indexit{309}
  `ClosureRing', 551
  Closures of (Sub)groups, \indexit{344}
  `Closure<Struct>', 281
  `ClosureSubgroup', 345
  `ClosureSubgroupNC', 345
  `Coboundaries', 642
  `Cochain', 641
  `CochainSpace', 641
  `Cocycles', 642
  cocycles, 370
  `CodePcGroup', 451
  `CodePcgs', 451
  Coding a Pc Presentation, \indexit{451}
  coefficient, binomial, 143
  Coefficient List Arithmetic, \indexit{211}
  `Coefficients', 588
  coefficients, for cyclotomics, 155
  `CoefficientsAndMagmaElements', 650
  `CoefficientsFamily', 672
  `CoefficientsMultiadic', 129
  `CoefficientsOfLaurentPolynomial', 664
  `CoefficientsOfUnivariatePolynomial', 658
  `Coefficients\-Of\-Univariate\-Rational\-Function', 658
  `CoefficientsQadic', 129
  `CoefficientsRing', 665
  `CoeffsCyc', 155
  `CoeffsMod', 212
  cohomology, 370
  `COHORTS_PRIMITIVE_GROUPS', 516
  `CoKernelOfAdditiveGeneralMapping', 304
  `CoKernelOfMultiplicativeGeneralMapping', 303
  `CollapsedMat', 799
  `Collected', 193
  Collection Families, \indexit{260}
  `CollectionsFamily', 260
  `ColumnIndexOfReesMatrixSemigroupElement', 533
  `Column\-Index\-Of\-Rees\-Zero\-Matrix\-Semigroup\-Element', 533
  `Combinations', 145
  Combinations, Arrangements and Tuples, \indexit{145}
  `CombinatorialCollector', 446
  Combinatorial Numbers, \indexit{143}
  `Comm', 289
    \sub for words, 326
  Command Line Options, \indexit{27}
  comments, 39
  `CommutativeDiagram', 796
  `CommutatorFactorGroup', 363
  `CommutatorLength', 353
    \sub for character tables, 720
  `CommutatorSubgroup', 352
  `Compacted', 193
  `CompanionMat', 228
  `CompareVersionNumbers', 830
  comparison, fp semigroup elements, 539
    \sub operation, 288
    \sub rational functions, 656
  Comparison of Associative Words, \indexit{326}
  Comparison of Class Functions, \indexit{753}
  Comparison of Elements of Finitely Presented Groups, \indexit{454}
  Comparison of Elements of Finitely Presented Semigroups, \indexit{539}
  Comparison of Permutations, \indexit{403}
  Comparison of Rational Functions, \indexit{656}
  Comparison of Words, \indexit{319}
  Comparison Operations for Elements, \indexit{288}
  Comparisons, \indexit{46}
  comparisons, of booleans, 165
    \sub of lists, 177
  Comparisons of Booleans, \indexit{165}
  Comparisons of Cyclotomics, \indexit{157}
  Comparisons of Lists, \indexit{177}
  Comparisons of Records, \indexit{257}
  Comparisons of Strings, \indexit{246}
  `CompatibleConjugacyClasses', 716
  `CompatiblePairs', 450
  Compilation, \indexit{815}
  Compiling Library Code, \indexit{35}
  `Complementclasses', 352
  `ComplementclassesEA', 372
  `ComplementIntMat', 234
  `ComplementSystem', 355
  Completion Files, \indexit{33}
  `ComplexConjugate', 160
    \sub for class functions, 756
  `ComplexificationQuat', 604
  Components of a Dixon Record, \indexit{738}
  `CompositionMapping', 297
    \sub for Frobenius automorphisms, 576
  `CompositionMapping2', 297
  `CompositionMaps', 793
  `CompositionOfStraightLinePrograms', 334
  `CompositionSeries', 360
    \sub for groups with pcgs, 441
  `ComputedBrauerTables', 712
  `ComputedClassFusions', 789
  `ComputedIndicators', 729
  `ComputedIsPSolvableCharacterTables', 729
  `ComputedPowerMaps', 785
  `ComputedPrimeBlockss', 725
  Computing a Pcgs, \indexit{426}
  Computing a Permutation Representation, \indexit{406}
  Computing Pc Groups, \indexit{447}
  Computing Possible Permutation Characters, \indexit{777}
  Computing the Irreducible Characters of a Group, \indexit{734}
  `Concatenation', 193
  concatenation, of lists, 193
  `Conductor', 155
  `ConfluentRws', 337
  `Congruences', for character tables, 801
  Congruences for semigroups, \indexit{529}
  `ConjugacyClass', 349
  Conjugacy Classes, \indexit{349}
  `ConjugacyClasses', attribute, 349
    \sub for character tables, 715
    \sub for groups with pcgs, 441
    \sub for linear groups, 504
  `ConjugacyClassesByOrbits', 350
  `ConjugacyClassesByRandomSearch', 350
  Conjugacy Classes in Classical Groups, \indexit{504}
  Conjugacy Classes in Solvable Groups, \indexit{441}
  `ConjugacyClassesMaximalSubgroups', 364
  `ConjugacyClassesPerfectSubgroups', 367
  `ConjugacyClassesSubgroups', 364
  `ConjugacyClassSubgroups', 363
  conjugate, matrix, 217
    \sub of a word, 326
  `ConjugateDominantWeight', 634
  `ConjugateDominantWeightWithWord', 634
  `ConjugateGroup', 342
  `Conjugates', 570
  `ConjugateSubgroup', 344
  `ConjugateSubgroups', 344
  conjugation, 388
  `ConjugatorAutomorphism', 380
  `ConjugatorAutomorphismNC', 380
  `ConjugatorIsomorphism', 380
  `ConjugatorOfConjugatorIsomorphism', 381
  `ConnectGroupAndCharacterTable', 716
  `ConsiderKernels', 801
  `ConsiderSmallerPowerMaps', 802
  `ConsiderStructureConstants', 793
  `ConsiderTableAutomorphisms', 804
  `ConstantTimeAccessList', 189
  constituent, of a group character, 760
  `ConstituentsCompositionMapping', 297
  `ConstituentsOfCharacter', 761
  Constructing Algebras as Free Algebras, \indexit{601}
  Constructing Algebras by Generators, \indexit{600}
  Constructing Algebras by Structure Constants, \indexit{602}
  Constructing Character Tables from Others, \indexit{740}
  Constructing Domains, \indexit{280}
  Constructing Lie algebras, \indexit{626}
  Constructing Pc Groups, \indexit{445}
  Constructing Subdomains, \indexit{284}
  Constructing Tables of Marks, \indexit{689}
  Constructing Vector Spaces, \indexit{584}
  Construction of Abelian Number Fields, \indexit{577}
  Construction of Stabilizer Chains, \indexit{411}
  Constructors for Basic Groups, \indexit{505}
  `ContainedCharacters', 800
  `ContainedDecomposables', 800
  `ContainedMaps', 795
  `ContainedPossibleCharacters', 798, 799
  `ContainedPossibleVirtualCharacters', 798, 799
  `ContainedSpecialVectors', 798, 799
  `ContainedTom', 698
  `ContainingTom', 698
  `continue' statement, 54
  Conventions for Character Tables, \indexit{715}
  convert, to a string, 245
  Converting Groups to Finitely Presented Groups, \indexit{462}
  `ConvertToCharacterTable', 713
  `ConvertToCharacterTableNC', 713
  `ConvertToMatrixRep', 229
  `ConvertToMatrixRepNC', 229
  `ConvertToRangeRep', 202
  `ConvertToStringRep', 245
  `ConvertToTableOfMarks', 693
  `ConvertToVectorRep', 210
  `ConvertToVectorRepNC', 210
  `ConwayPolynomial', 576
  Conway Polynomials, \indexit{576}
  coprime, 47
  copy, 113
    \sub an object, 113
  `CopyOptionsDefaults', 416
  Copyrights, \indexit{827}
  `CopyStabChain', 415
  `Core', 351
  `CorrespondingGeneratorsByModuloPcgs', 434
  coset, 346
  `CosetLeadersMatFFE', 213
  Cosets, \indexit{346}
  `CosetTable', 457
  `CosetTableBySubgroup', 458
  `CosetTableDefaultLimit', 459
  `CosetTableDefaultMaxLimit', 458
  `CosetTableFromGensAndRels', 458
  `CosetTableInWholeGroup', 461
  `CosetTableOfFpSemigroup', 542
  Coset Tables and Coset Enumeration, \indexit{457}
  Coset tables for subgroups in the whole group, \indexit{461}
  `CosetTableStandard', 460
  CRC, 36
  `CrcFile', 94
    \sub example, 36
  CRC Numbers, \indexit{36}
  `CreateCompletionFiles', 34
  `CreateCompletionFilesPkg', 832
  Creating Character Tables, \indexit{711}
  Creating Class Functions from Values Lists, \indexit{757}
  Creating Class Functions using Groups, \indexit{758}
  Creating Finite Fields, \indexit{574}
  Creating Finitely Presented Groups, \indexit{454}
  Creating Finitely Presented Semigroups, \indexit{538}
  Creating Group Homomorphisms, \indexit{375}
  Creating Groups, \indexit{341}
  Creating Mappings, \indexit{296}
  Creating Permutations, \indexit{404}
  Creating Presentations, \indexit{471}
  Creation of Algebraic Extensions, \indexit{677}
  Creation of Rational Functions, \indexit{674}
  Credit, \indexit{21}
  `CrystGroupDefaultAction', 425
  `Cycle', 396
  `CycleLength', 396
  `CycleLengths', 396
  `Cycles', 396
  `CycleStructureClass', 762
  `CycleStructurePerm', 404
  `CyclicExtensionsTom', 698
  `CyclicGroup', 499
  `CyclotomicField', 577
  cyclotomic field elements, 153
  cyclotomic fields, canonicalbasis, 579
  `CyclotomicPolynomial', 662
  Cyclotomic Polynomials, \indexit{662}
  `Cyclotomics', 153
  cyclotomics, defaultfield, 578
\letter D
  $d_N$, 157
  Darstellungsgruppe, see `EpimorphismSchurCover', 372
  `DataType', 124
  data type, unknown, 163
  `DayDMY', 251
  `DaysInMonth', 251
  `DaysInYear', 251
  Debugging Recursion, \indexit{83}
  DEC, 237
  `DeclareAutoPackage', 832
  `DeclareHandlingByNiceBasis', 598
  `DeclareInfoClass', 78
  `DeclarePackage', 832
  `DeclarePackageAutoDocumentation', 832
  `DeclarePackageDocumentation', 832
  `DecodeTree', 488
  DecodeTree, \indexit{488}
  decompose, a group character, 760
  `DecomposedFixedPointVector', 699
  `DecomposeTensorProduct', 642
  `Decomposition', 237
  `DecompositionInt', 238
  `DecompositionMatrix', 727
  decomposition matrix, 237
  Decompositions, \indexit{237}
  `Decreased', 769
  `DefaultField', 566
    \sub for cyclotomics, 156
    \sub for finite field elements, 574
  `DefaultFieldByGenerators', 567
  `DefaultFieldOfMatrix', 218
  `DefaultFieldOfMatrixGroup', 420
  `DefaultRing', 550
    \sub for finite field elements, 574
  `DefaultRingByGenerators', 551
  `DefaultStabChainOptions', 413
  Defining a Pcgs Yourself, \indexit{427}
  `DefiningPolynomial', 568
  `DefiningQuotientHomomorphism', 466
  `DegreeFFE', 573
  `DegreeIndeterminate', 660
  `DegreeOfBinaryRelation', 308
  `DegreeOfCharacter', 760
  `DegreeOfLaurentPolynomial', 659
  `DegreeOfTransformation', 543
  `DegreeOfTransformationSemigroup', 529
  `DegreeOverPrimeField', 568
  `Delta', 807
  denominator, of a rational, 142
  `DenominatorCyc', 155
  `DenominatorOfModuloPcgs', 433
  `DenominatorOfRationalFunction', 657
  `DenominatorRat', 142
  deprecated, 832
  `DepthOfPcElement', 429
  `DepthOfUpperTriangularMatrix', 227
  `Derangements', 147
  `Derivations', 627
  `Derivative', 661
  `DerivedLength', 360
  `DerivedSeriesOfGroup', 360
  `DerivedSubgroup', 352
  `DerivedSubgroupsTom', 697
  `DerivedSubgroupsTomPossible', 697
  `DerivedSubgroupsTomUnique', 697
  `DerivedSubgroupTom', 697
  `DescriptionOfRootOfUnity', 156
  `Determinant', 218
  determinant character, 762
  `DeterminantIntMat', 237
  `DeterminantMat', 218
  `DeterminantMatDestructive', 219
  `DeterminantMatDivFree', 219
  Determinant of an integer matrix, \indexit{237}
  `DeterminantOfCharacter', 762
  Developing rewriting systems, \indexit{339}
  `DiagonalizeIntMat', 235
  `DiagonalizeMat', 224
  `DiagonalMat', 220
  `DiagonalOfMat', 226
  `Difference', 268
  `DifferenceBlist', 205
  `DihedralGroup', 500
  `Dimension', 564
  `DimensionOfHighestWeightModule', 643
  `DimensionOfMatrixGroup', 420
  `DimensionOfVectors', 593
  `DimensionsLoewyFactors', 361
  `DimensionsMat', 218
  Directories, \indexit{90}
  `DirectoriesLibrary', 90
  `DirectoriesPackageLibrary', 830
  `DirectoriesPackagePrograms', 830
  `DirectoriesSystemPrograms', 91
  `Directory', 90
  `DirectoryContents', 91
  `DirectoryCurrent', 90
  `DirectoryTemporary', 90
  `DirectProduct', 494
  `DirectProductOp', 494
  Direct Products, \indexit{494}
  `DirectSumDecomposition', 612
    \sub for Lie algebras, 631
  Direct Sum Decompositions, \indexit{630}
  `DirectSumOfAlgebraModules', 623
    \sub for Lie algebras, 646
  `DirectSumOfAlgebras', 611
  `DisableAttributeValueStoring', 122
  disable automatic loading, 828
  `Discriminant', 661
  `Display', 65
    \sub for character tables, 731, 756
    \sub for tables of marks, 691
  `DisplayCacheStats', 82
  `DisplayCompositionSeries', 360
  `DisplayEggBoxOfDClass', 531
  `DisplayImfInvariants', 520
  `DisplayInformationPerfectGroups', 513
  `DisplayOptions', 732
  `DisplayOptionsStack', 88
  `DisplayProfile', 81
  `DisplayRevision', 82
  `DistancesDistributionMatFFEVecFFE', 212
  `DistancesDistributionVecFFEsVecFFE', 212
  `DistanceVecFFE', 212
  Distinguished Subalgebras, \indexit{628}
  division, 47
    \sub operation, 289
  `DivisionRingByGenerators', 567
  division rings, 566
  divisors, of an integer, 132
  `DivisorsInt', 132
  Dixon-Schneider algorithm, 736
  `DixonInit', 737
  `DixonRecord', 737
  `DixonSplit', 737
  `DixontinI', 737
  `DMYDay', 251
  `DMYhmsSeconds', 252
  `DnLattice', 770
  `DnLatticeIterative', 771
  `do', 51
  document formats (text, dvi, ps, pdf, html), 23
  `Domain', 285
  `DomainByGenerators', 285
  Domain Categories, \indexit{282}
  Domains, \indexit{110}
  Domains Generated by Class Functions, \indexit{783}
  Domains of Subspaces of Vector Spaces, \indexit{585}
  `DominantCharacter', 642
  `DominantWeights', 642
  `DoubleCoset', 348
  `DoubleCosetRepsAndSizes', 349
  Double Cosets, \indexit{348}
  `DoubleCosets', operation, 348
  `DoubleCosetsNC', operation, 348
  doublequote character, 244
  doublequotes, 242
  `DownEnv', 69
  Dummy Streams, \indexit{105}
  duplicate free, 188
  `DuplicateFreeList', 193
  Duplication of Lists, \indexit{175}
  Duplication of Objects, \indexit{113}
  `DxIncludeIrreducibles', 738
\letter E
  `E', 153
  $e_N$, 157
  `EANormalSeriesByPcgs', 435
  `Earns', 397
  `EB', 157
  `EC', 157
  Echelonized Matrices, \indexit{224}
  `ED', 157
  `Edit', 73
  Editing Files, \indexit{73}
  Editor Support, \indexit{73}
  `EE', 157
  `EF', 157
  Efficiency of Homomorphisms, \indexit{378}
  `EG', 157
  `EggBoxOfDClass', 531
  `EH', 157
  `EI', 158
  `Eigenspaces', 223
  `Eigenvalues', 223
  `EigenvaluesChar', 763
  `Eigenvectors', 223
  Eigenvectors and eigenvalues, \indexit{223}
  `EJ', 158
  `EK', 158
  `EL', 158
  `ElementaryAbelianGroup', 500
  `ElementaryAbelianSeries', 360
  `ElementaryAbelianSeriesLargeSteps', 360
  Elementary Divisors, \indexit{223}
  `ElementaryDivisorsMat', 224
  `ElementaryDivisorsMatDestructive', 224
  Elementary Operations for a Pcgs, \indexit{428}
  Elementary Operations for a Pcgs and an Element, \indexit{428}
  Elementary Operations for Integers, \indexit{125}
  Elementary Operations for Rationals, \indexit{141}
  Elementary Tietze Transformations, \indexit{482}
  `ElementOfFpGroup', 456
  `ElementOfFpSemigroup', 540
  `ElementOfMagmaRing', 650
  `ElementOrdersPowerMap', 786
  `ElementProperty', 417
  `Elements', 265
  elements, definition, 109
    \sub of a list or collection, 265
  Elements as equivalence classes, \indexit{109}
  `ElementsFamily', 260
  Elements in Algebraic Extensions, \indexit{677}
  Elements of Free Magma Rings, \indexit{649}
  Elements of pc groups, \indexit{444}
  `ElementsStabChain', 415
  Elements with Prescribed Images, \indexit{392}
  element test, for lists, 177
  `elif', 50
  `EliminatedWord', 328
  `EliminationOrdering', 670
  `else', 50
  `EM', 158
  `emacs', 73
  `Embedding', 298
    \sub example for direct products, 494
    \sub example for semidirect products, 496
    \sub example for wreath products, 497
    \sub for group products, 498
    \sub for Lie algebras, 626
    \sub for magma rings, 650
  embeddings, find all, 384
  Embeddings and Projections for Group Products, \indexit{498}
  `EmptyBinaryRelation', 307
  `EmptyMatrix', 220
  `EmptySCTable', 602
  `EmptyStabChain', 416
  `EnableAttributeValueStoring', 122
  `End', 596
  `end', 54
  Enlarging Internally Represented Lists, \indexit{177}
  `Enumerator', 261
  `EnumeratorByBasis', 589
  `EnumeratorByFunctions', 261
  Enumerators, \indexit{203}
  `EnumeratorSorted', 261
  environment, 54
  `EpimorphismNilpotentQuotient', 468
  `EpimorphismPGroup', 468
  `EpimorphismQuotientSystem', 467
  epimorphisms, find all, 384
  `EpimorphismSchurCover', 372
  equality, associative words, 326
    \sub elements of finitely presented groups, 454
    \sub nonassociative words, 319
    \sub of records, 257
    \sub operation, 288
    \sub pcwords, 444
  Equality and Comparison of Domains, \indexit{280}
  equality test, 46
    \sub for permutations, 403
  equivalence class, 310
  Equivalence Classes, \indexit{310}
  `EquivalenceClasses', attribute, 311
  `EquivalenceClassOfElement', 311
  `EquivalenceClassOfElementNC', 311
  `EquivalenceClassRelation', 311
  equivalence relation, 308, 309
  `EquivalenceRelationByPairs', 310
  `EquivalenceRelationByPairsNC', 310
  `EquivalenceRelationByPartition', 310
  `EquivalenceRelationByPartitionNC', 310
  `EquivalenceRelationByProperty', 310
  `EquivalenceRelationByRelation', 310
  `EquivalenceRelationPartition', 310
  Equivalence Relations, \indexit{309}
  `ER', 158
  `Error', 71
  Error, \indexit{71}
  `ErrorCount', 71
  ErrorCount, \indexit{71}
  `ErrorNoTraceBack', 67
  errors, syntax, 63
  `ES', 158
  escaped characters, 244
  escaping non-special characters, 244
  `ET', 158
  `EU', 158
  `EuclideanDegree', 558
  `EuclideanQuotient', 558
  `EuclideanRemainder', 558
  Euclidean Rings, \indexit{558}
  Euler's totient function, 134
  `EulerianFunction', 359
  `EulerianFunctionByTom', 699
  `EV', 158
  `EvalStraightLineProgElm', 335
  `EvalString', 251
  evaluation, 41
    \sub strings, 250
  `EW', 158
  `EX', 158
  `ExactSizeConsiderFunction', 369
  `Exec', 108
  Exec, \indexit{108}
  execution, 48
  exit, 71
  expanded form of monomials, 673
  Expert Windows installation, \indexit{826}
  `Exponent', 359
    \sub for character tables, 720
  exponent, of the prime residue group, 134
  exponentiation, operation, 289
  `ExponentOfPcElement', 428
  `ExponentsConjugateLayer', 430
  `ExponentsOfCommutator', 430
  `ExponentsOfConjugate', 430
  `ExponentsOfPcElement', 428
  `ExponentsOfRelativePower', 430
  Exponents of Special Products, \indexit{430}
  `ExponentSumWord', 327
  `ExponentSyllable', 328
  Expressing Group Elements as Words in Generators, \indexit{345}
  Expressions, \indexit{41}
  `ExtendedPcgs', 432
  `ExtendStabChain', 416
  `Extension', 449
  `ExtensionNC', 449
  `ExtensionRepresentatives', 450
  `Extensions', 449
  Extensions of the p-adic Numbers, \indexit{680}
  `ExteriorPowerOfAlgebraModule', 646
  `ExternalOrbit', 400
  `ExternalOrbits', 400
  `ExternalOrbitsStabilizers', 400
  External Representation for Nonassociative Words, \indexit{322}
  external representation of polynomials, 673
  `ExternalSet', 399
  External Sets, \indexit{399}
  `ExternalSubset', 400
  `Extract', 767
  `ExtraspecialGroup', 500
  `ExtRepDenominatorRatFun', 674
  `ExtRepNumeratorRatFun', 674
  `ExtRepOfObj', external representation, for cyclotomics, 156
  `ExtRepPolynomialRatFun', 674
  `EY', 158
\letter F
  $f_N$, 157
  `FactorCosetAction', 395
    \sub for fp groups, 458
  `FactorCosetOperation', 458
  `FactorFreeSemigroupByRelations', 538
  `FactorGroup', 362
  `FactorGroupFpGroupByRels', 454
  `FactorGroupNC', 362
  `FactorGroupNormalSubgroupClasses', 748
  Factor Groups, \indexit{362}
  Factor Groups of Polycyclic Groups - Modulo Pcgs, \indexit{432}
  Factor Groups of Polycyclic Groups in their Own Representation, \indexit{434}
  `FactorGroupTom', 700
  `Factorial', 143
  `Factorization', 346
  factorization, 345
  `Factors', 558
    \sub of univariate polynomial, 662
  `FactorsInt', 131
  `FactorsOfDirectProduct', 741
  `FactorsSquarefree', 663
  Fail, \indexit{165}
  `fail', 165
  `FaithfulModule', 622
    \sub for Lie algebras, 640
  Families, \indexit{115}
  `FamiliesOfGeneralMappingsAndRanges', 306
  `FamiliesOfRows', 747
  `FamilyForOrdering', 274
  `FamilyObj', 115
  `FamilyPcgs', 443
  `FamilyRange', 306
  `FamilySource', 306
  FAQ, 818
  features, under UNIX, 27
  `fi', 50
  `Fibonacci', 151
  Fibonacci and Lucas Sequences, \indexit{151}
  `Field', 566
  `FieldExtension', 568
  field homomorphisms, Frobenius, 576
  `FieldOfMatrixGroup', 420
  `FieldOverItselfByGenerators', 567
  fields, 566
  File Access, \indexit{92}
  `FileDescriptorOfStream', 97
  `Filename', 91
  Filename, \indexit{91}
  File Operations, \indexit{93}
  File Streams, \indexit{102}
  `Filtered', 196
  Filters, \indexit{116}
  Filters Controlling the Arithmetic Behaviour of Lists, \indexit{179}
  Finding Positions in Lists, \indexit{185}
  Finding Submodules, \indexit{683}
  `FindSl2', 638
  Finish Installation and Cleanup, \indexit{817}
  Finite Field Elements, \indexit{572}
  Finitely Presented Lie Algebras, \indexit{638}
  Finitely presented monoids, \indexit{540}
  finiteness test, for a list or collection, 265
  Finite Perfect Groups, \indexit{511}
  `First', 197
  `FittingSubgroup', 353
  `Flat', 194
  flush character, 244
  For, \indexit{51}
  `ForAll', 198
  `ForAny', 198
  `for' loop, 51
  `FpElmComparisonMethod', 455
  `FpGroupPresentation', 471
  `FpGrpMonSmgOfFpGrpMonSmgElement', 538
  `FpLieAlgebraByCartanMatrix', 639
  frame, 772
  `FrattiniSubgroup', 353
    \sub for groups with pcgs, 441
  `FreeAlgebra', 601
  `FreeAlgebraWithOne', 601
  `FreeAssociativeAlgebra', 601
  `FreeAssociativeAlgebraWithOne', 601
  `FreeGeneratorsOfFpGroup', 455
  `FreeGeneratorsOfFpSemigroup', 539
  `FreeGeneratorsOfWholeGroup', 455
  `FreeGroup', 323
  `FreeGroupOfFpGroup', 455
  Free Groups, Monoids and Semigroups, \indexit{323}
  `FreeLeftModule', 564
  `FreeLieAlgebra', 627
  `FreeMagma', 321
  `FreeMagmaRing', 648
  Free Magma Rings, \indexit{648}
  Free Magmas, \indexit{321}
  `FreeMagmaWithOne', 321
  Free Modules, \indexit{563}
  `FreeMonoid', 534
    \sub with example, 324
  `FreeMonoidOfRewritingSystem', 542
  `FreeSemigroup', 324
    \sub with examples, 528
  `FreeSemigroupOfFpSemigroup', 539
  `FreeSemigroupOfRewritingSystem', 542
  Frobenius automorphism, 576
  `FrobeniusAutomorphism', 576
  FrobeniusAutomorphism, \indexit{576}
  `FrobeniusCharacterValue', 781
  `FullMatrixAlgebra', 604
  `FullMatrixAlgebraCentralizer', 612
  `FullMatrixLieAlgebra', 627
  `FullMatrixModule', 565
  `FullMatrixSpace', 593
  `FullRowModule', 565
  `FullRowSpace', 593
  `FullTransformationSemigroup', 529
  Function, \indexit{54}
  `function', 54
  `FunctionAction', 399
  function call, 45
    \sub with arguments, 45
    \sub with options, 45
  Function Calls, \indexit{45}
  `FunctionOperation', 832
  functions, 60, 296
    \sub definition by arrow notation, 56
    \sub definition of, 54
    \sub recursive, 54
    \sub with a variable number of arguments, 45, 55
  `FunctionsFamily', 62
  Functions for Coding Theory, \indexit{212}
  Functions for GAP Packages, \indexit{829}
  Functions that do nothing, \indexit{61}
  Function that Modify Boolean Lists, \indexit{206}
  Function Types, \indexit{61}
  `FusionCharTableTom', 706
  `FusionConjugacyClasses', 788
  `FusionConjugacyClassesOp', 788
  fusions, 788
  `FusionsAllowedByRestrictions', 804
  `FusionsTom', 695
\letter G
  $G$-sets, 387, 399
  $g_N$, 157
  `gac', 34
  Galois Action, \indexit{568}
  Galois Conjugacy of Cyclotomics, \indexit{159}
  `GaloisCyc', 159
    \sub for class functions, 756
  `GaloisField', 575
  `GaloisGroup', of field, 569
    \sub of rational class of a group, 351
  Galois Groups of Abelian Number Fields, \indexit{581}
  `GaloisMat', 161
  `GaloisStabilizer', 579
  `GaloisType', 663
  `gap.rc', 31, 33
  GAP3, 33
  `Gap3CatalogueIdGroup', 509
  GAP for Macintosh OS X, \indexit{822}
  GAP for MacOS, \indexit{823}
  `GAPInfo', 833
  `GAPInfo.RootPaths', 29
  `GapInputPcGroup', 448
  `GapInputSCTable', 602
  `GAPKB_REW', 541
  GAP Root Directory, \indexit{89}
  `GasmanLimits', 85
  `GasmanMessageStatus', 85
  `GasmanStatistics', 85
  Gaussian algorithm, 222
  `GaussianIntegers', 583
  `GaussianRationals', 578
  Gaussians, \indexit{583}
  `Gcd', 559
  Gcd and Lcm, \indexit{559}
  `Gcdex', 129
  `GcdInt', 128
  `GcdOp', 559
  `GcdRepresentation', 559
  `GcdRepresentationOp', 559
  General Binary Relations, \indexit{307}
  `GeneralisedEigenspaces', 223
  `GeneralisedEigenvalues', 223
  generalized characters, 750
  `GeneralizedEigenspaces', 223
  `GeneralizedEigenvalues', 223
  `GeneralLinearGroup', 501
  `GeneralMappingByElements', 296
  General Mappings, \indexit{305}
  `GeneralMappingsFamily', 306
  `GeneralOrthogonalGroup', 503
  `GeneralUnitaryGroup', 502
  Generating Fields, \indexit{566}
  Generating modules, \indexit{562}
  Generating Rings, \indexit{550}
  generator, of the prime residue group, 136
  `GeneratorsOfAdditiveGroup', 548
  `GeneratorsOfAdditiveMagma', 548
  `GeneratorsOfAdditiveMagmaWithZero', 548
  `GeneratorsOfAlgebra', 608
  `GeneratorsOfAlgebraModule', 619
  `GeneratorsOfAlgebraWithOne', 608
  `GeneratorsOfDivisionRing', 567
  `GeneratorsOfDomain', 284
  `Generators\-Of\-Equivalence\-Relation\-Partition', 310
  `GeneratorsOfField', 567
  `GeneratorsOfGroup', 342
  `GeneratorsOfIdeal', 553
  `GeneratorsOfLeftIdeal', 554
  `GeneratorsOfLeftModule', 562
  `GeneratorsOfLeftOperatorAdditiveGroup', 562
  `GeneratorsOfLeftVectorSpace', 585
  `GeneratorsOfMagma', 315
  `GeneratorsOfMagmaWithInverses', 315
  `GeneratorsOfMagmaWithOne', 315
  `GeneratorsOfMonoid', 534
  `GeneratorsOfNearAdditiveGroup', 548
  `GeneratorsOfNearAdditiveMagma', 548
  `GeneratorsOfNearAdditiveMagmaWithZero', 548
  `GeneratorsOfPresentation', 471
  `GeneratorsOfRightIdeal', 554
  `GeneratorsOfRightModule', 563
  `GeneratorsOfRightOperatorAdditiveGroup', 562
  `GeneratorsOfRing', 551
  `GeneratorsOfRingWithOne', 555
  `GeneratorsOfRws', 337
  `GeneratorsOfSemigroup', 527
  `GeneratorsOf<Struct>', 281
  `GeneratorsOfTwoSidedIdeal', 553
  `GeneratorsOfVectorSpace', 585
  `GeneratorsPrimeResidues', 135
  `GeneratorsSmallest', 369
  `GeneratorsSubgroupsTom', 703
  `GeneratorSyllable', 328
  Generic Construction of Tables of Marks, \indexit{707}
  `GetFusionMap', 790
  Get the Archives, \indexit{813}
  getting help, 22
  `GF', 575
  `GL', 501
  GL and SL, \indexit{421}
  Global Memory Information, \indexit{85}
  `GModuleByMats', 682
  `GO', 503
  `GQuotients', 384
  `Grading', 613
  Green's Relations, \indexit{530}
  `GreensDClasses', 531
  `GreensDClassOfElement', 531
  `GreensDRelation', 530
  `GreensHClasses', 531
  `GreensHClassOfElement', 531
  `GreensHRelation', 530
  `GreensJClasses', 531
  `GreensJClassOfElement', 531
  `GreensJRelation', 530
  `GreensLClasses', 531
  `GreensLClassOfElement', 531
  `GreensLRelation', 530
  `GreensRClasses', 531
  `GreensRClassOfElement', 531
  `GreensRRelation', 530
  Groebner Bases, \indexit{671}
  `GroebnerBasis', 671
  `GroebnerBasisNC', 671
  `Group', 341
  group actions, 387, 388
    \sub operations syntax, 387
  Group Actions - Name Changes, \indexit{832}
  group algebra, 648
  Group Automorphisms, \indexit{380}
  `GroupByRws', 446
  `GroupByRwsNC', 446
  group characters, 750
  Group Elements, \indexit{341}
  `GroupGeneralMappingByImages', 376
  `GroupHClassOfGreensDClass', 532
  `GroupHomomorphismByFunction', 376
  `GroupHomomorphismByImages', 375
  `GroupHomomorphismByImagesNC', 375
  `GroupOfPcgs', 428
  group operations, 388, 832
  Group Properties, \indexit{356}
  `GroupRing', 648
  group ring, 648
  Groups of Automorphisms, \indexit{382}
  `GroupStabChain', 414
  `GroupWithGenerators', 342
  `GU', 502
\letter H
  $h_N$, 157
  `HallSubgroup', 354
  `HallSystem', 355
    \sub for groups with pcgs, 441
  Handling of Streams in the Background, \indexit{105}
  `HasAbelianFactorGroup', 363
  `HasElementaryAbelianFactorGroup', 363
  `HasIndeterminateName', 655
  `HasParent', 283
  `HasseDiagramBinaryRelation', 309
  `HeadPcElementByNumber', 430
  `HenselBound', 664
  hermite normal form, 832
  `HermiteNormalFormIntegerMat', 235
  `HermiteNormalFormIntegerMatTransform', 235
  `HeuristicCancelPolynomials', 676
  `HexStringInt', 247
  `HighestWeightModule', 645
  History of Character Theory Stuff in GAP, \indexit{710}
  `HMSMSec', 252
  `Hom', 596
  `HomeEnumerator', 399
  Homomorphism for very large groups, \indexit{379}
  `HomomorphismQuotientSemigroup', 530
  homomorphisms, find all, 383
  homomorphisms, Frobenius, field, 576
  Homomorphisms of Algebras, \indexit{613}
  `HomomorphismTransformationSemigroup', 529
  How to Implement New Kinds of Vector Spaces, \indexit{598}
  `HumanReadableDefinition', 701
\letter I
  $i_N$, 158
  `Ideal', 552
  `IdealByGenerators', 553
  `IdealNC', 553
  Ideals, \indexit{606}
  Ideals in Rings, \indexit{552}
  Ideals of semigroups, \indexit{529}
  `Idempotents', 316
  `IdempotentsTom', 695
  `IdempotentsTomInfo', 695
  Identical Lists, \indexit{174}
  Identical Objects, \indexit{110}
  Identical Records, \indexit{256}
  `IdentificationOfConjugacyClasses', 716
  `Identifier', for character tables, 722
    \sub for tables of marks, 695
  Identifiers, \indexit{40}
  `Identity', 285
  `IdentityBinaryRelation', 307
  `IdentityFromSCTable', 603
  `IdentityMapping', 298
  `IdentityMat', 219
  `IdentityTransformation', 543
  `IdFunc', 61
  `IdGap3SolvableGroup', 509
  `IdGroup', 509
  `IdSmallGroup', 509
  `IdsOfAllSmallGroups', 509
  If, \indexit{50}
  `if' statement, 50
  If Things Go Wrong, \indexit{818}
  `Image', 299
    \sub for Frobenius automorphisms, 576
  image, vector under matrix, 217
  `ImageElm', 299
  `ImageListOfTransformation', 543
  `Images', 300
  `ImagesElm', 299
  `ImageSetOfTransformation', 544
  `ImagesRepresentative', 299
  `ImagesSet', 299
  `ImagesSmallestGenerators', 379
  `ImagesSource', 299
  Images under Mappings, \indexit{299}
  `ImfInvariants', 522
  `ImfMatrixGroup', 523
  `ImfNumberQClasses', 520
  `ImfNumberQQClasses', 520
  `ImfNumberZClasses', 520
  `Immutable', 112
  `ImmutableBasis', 591
  `ImmutableMatrix', 229
  `in', for collections, 268
    \sub for lists, 177
    \sub for strictly sorted lists, 191
    \sub operation for, 268
  `IndependentGeneratorsOfAbelianGroup', 370
  `Indeterminate', 654
  `IndeterminateName', 655
  `Indeterminateness', 798
  `IndeterminateNumberOfLaurentPolynomial', 665
  `Indeterminate\-Number\-Of\-Univariate\-Rational\-Function', 655
  `Indeterminate\-Of\-Univariate\-Rational\-Function', 655
  Indeterminates, \indexit{654}
  `IndeterminatesOfPolynomialRing', 665
  `Index', 343
  `IndexInWholeGroup', 343
  `IndexNC', 343
  Index numbers of primitive groups, \indexit{517}
  `Indicator', 729
  `IndicatorOp', 729
  `IndicesCentralNormalSteps', 435
  `IndicesChiefNormalSteps', 436
  `IndicesEANormalSteps', 435
  `IndicesInvolutaryGenerators', 460
  `IndicesNormalSteps', 437
  `IndicesOfAdjointBasis', 609
  `IndicesPCentralNormalStepsPGroup', 436
  `IndicesStabChain', 415
  `Indirected', 794
  Induced Actions, \indexit{684}
  `InducedAutomorphism', 382
  `InducedClassFunction', 764
  `InducedClassFunctions', 764
  `InducedCyclic', 765
  `InducedPcgs', 431
  `InducedPcgsByGenerators', 431
  `InducedPcgsByGeneratorsNC', 431
  `InducedPcgsByPcSequence', 431
  `InducedPcgsByPcSequenceAndGenerators', 431
  `InducedPcgsByPcSequenceNC', 431
  `InducedPcgsWrtFamilyPcgs', 443
  `InducedPcgsWrtSpecialPcgs', 439
  `Inequalities', 781
  inequality, of records, 257
  inequality test, 46
  `InertiaSubgroup', 761
  Infinity, \indexit{156}
  `infinity', 156
  inflated class functions, 763
  `Info', 78
  `InfoAlgebra', 600
  `InfoAttributes', 122
  `InfoBckt', 417
  `InfoCharacterTable', 714
  `InfoCoh', 372
  `InfoComplement', 352
  `InfoCoset', 349
  `InfoFpGroup', 454
  Info Functions, \indexit{78}
  `InfoGroebner', 672
  `InfoGroup', 342
  `InfoLattice', 367
  `InfoLevel', 78
  `InfoMatrix', 215
  `InfoMonomial', 806
  `InfoNumtheor', 134
  `InfoOptions', 88
  `InfoPcSubgroup', 369
  Information about a function, \indexit{60}
  Information about the version used, \indexit{82}
  `InfoText', 723
  `InfoTom', 693
  `InfoWarning', 79
  `InitFusion', 803
  `InitPowerMap', 801
  `InjectionZeroMagma', 314
  `InnerAutomorphism', 381
  `InnerAutomorphismNC', 381
  `InnerAutomorphismsAutomorphismGroup', 382
  inner product, of group characters, 760
  Input-Output Streams, \indexit{103}
  `InputLogTo', 94
    \sub for streams, 101
    \sub stop logging input, 94
  `InputOutputLocalProcess', 104
  `InputTextFile', 102
  `InputTextNone', 105
  `InputTextString', 103
  `InputTextUser', 102
  `InsertTrivialStabilizer', 416
  `InstallAtExit', 71
  installation, 813
  Installation of GAP for MacOS, \indexit{824}
  Installation Overview, \indexit{813}
  `InstallCharReadHookFunc', 105
  `InstalledPackageVersion', 830
  `InstallFactorMaintenance', 291
  `InstallHandlingByNiceBasis', 598
  Installing a GAP Package, \indexit{828}
  `InstallIsomorphismMaintenance', 291
  `InstallSubsetMaintenance', 291
  `Int', 125
    \sub for cyclotomics, 154
    \sub for strings, 250
  `INT_CHAR', 249
  integer part of a quotient, 128
  `Integers', 125
  Integral Bases of Abelian Number Fields, \indexit{579}
  `IntegralizedMat', 238
  `IntegratedStraightLineProgram', 334
  `IntermediateGroup', 362
  `IntermediateSubgroups', 362
  Internally Represented Cyclotomics, \indexit{162}
  Internally Represented Strings, \indexit{245}
  `InterpolatedPolynomial', 561
  `IntersectBlist', 206
  `Intersection', 267
    \sub for groups with pcgs, 441
  intersection, of collections, 267
    \sub of sets, 192
  `Intersection2', 267
  `IntersectionBlist', 205
  `IntersectionsTom', 699
  `IntersectSet', 192
  `IntFFE', 574
  `IntFFESymm', 574
  `IntHexString', 250
  `IntScalarProducts', 798, 799
  `IntVecFFE', 574
  `InvariantBilinearForm', 422
  `InvariantElementaryAbelianSeries', 361
  Invariant Forms, \indexit{422}, \indexit{685}
  `InvariantLattice', 424
  `InvariantQuadraticForm', 422
  `InvariantSesquilinearForm', 422
  `Invariant\-Subgroups\-Elementary\-Abelian\-Group', 368
  `Inverse', 287
  inverse, group homomorphism, 377
    \sub matrix, 217
    \sub of class function, 755
  `InverseAttr', 287
  `InverseClasses', 723
  `InverseGeneralMapping', 297
  `InverseImmutable', 287
  `InverseMap', 793
  `InverseMatMod', 231
  `InverseMutable', 287
  `InverseOp', 287
  `InverseRepresentative', 415
  `InverseSameMutability', 287
  `InverseSM', 287
  Invoking the Help, \indexit{22}
  `Irr', 718
  irrationalities, 153
  `IrrBaumClausen', 734
  `IrrConlon', 734
  `IrrDixonSchneider', 734
  Irreducibility Tests, \indexit{683}
  irreducible character, 759
  irreducible characters, computation, 737
  `IrreducibleDifferences', 766
  Irreducible Maximal Finite Integral Matrix Groups, \indexit{518}
  `IrreducibleModules', 736
    \sub for groups with pcgs, 441
  `IrreducibleRepresentations', 735
  `IrreducibleRepresentationsDixon', 736
  `IrreducibleSolvableGroup', 518
  `IrreducibleSolvableGroupMS', 517
  Irreducible Solvable Matrix Groups, \indexit{517}
  `Is16BitsFamily', 330
  `Is32BitsFamily', 330
  `Is8BitsFamily', 330
  `IsAbelian', 316
    \sub for character tables, 720
  `IsAbelianNumberField', 578
  `IsAbelianNumberFieldPolynomialRing', 667
  `IsAbelianTom', 697
  `IsAdditiveElement', 292
  `IsAdditiveElementWithInverse', 292
  `IsAdditiveElementWithZero', 292
  `IsAdditiveGroup', 547
  `IsAdditiveGroupGeneralMapping', 304
  `IsAdditiveGroupHomomorphism', 304
  `IsAdditivelyCommutative', 548
  `IsAdditivelyCommutativeElement', 294
  `IsAdditivelyCommutativeElementCollColl', 294
  `Is\-Additively\-Commutative\-Element\-Collection', 294
  `IsAdditivelyCommutativeElementFamily', 294
  `IsAdditiveMagma', 546
  `IsAdditiveMagmaWithInverses', 547
  `IsAdditiveMagmaWithZero', 546
  `IsAlgebra', 607
  `IsAlgebraGeneralMapping', 305
  `IsAlgebraHomomorphism', 305
  `IsAlgebraicElement', 678
  `IsAlgebraicExtension', 677
  `IsAlgebraModuleElement', 619
  `IsAlgebraModuleElementCollection', 619
  `IsAlgebraModuleElementFamily', 619
  `IsAlgebraWithOne', 607
  `IsAlgebraWithOneGeneralMapping', 305
  `IsAlgebraWithOneHomomorphism', 305
  `IsAlphaChar', 246
  `IsAlternatingGroup', 408
  `IsAnticommutative', 556
  `IsAntisymmetricBinaryRelation', 308
  `IsAssociated', 556
  `IsAssociative', 316
  `IsAssociativeElement', 294
  `IsAssociativeElementCollColl', 294
  `IsAssociativeElementCollection', 294
  `IsAssocWord', 323
  `IsAssocWordWithInverse', 323
  `IsAssocWordWithOne', 323
  `IsAutomorphismGroup', 382
  `IsBasicWreathLessThanOrEqual', 326
  `IsBasicWreathProductOrdering', 278
  `IsBasis', 587
  `IsBasisByNiceBasis', 598
  `IsBasisOfAlgebraModuleElementSpace', 620
  `IsBergerCondition', 807
  `IsBijective', 299
  `IsBinaryRelation', 307
    \sub same as `IsEndoGeneralMapping', 307
  `IsBLetterAssocWordRep', 329
  `IsBLetterWordsFamily', 329
  `IsBlist', 204
  `IsBlockMatrixRep', 231
  `IsBool', 165
  `IsBound', for lists, 173
  IsBound and Unbind for Lists, \indexit{173}
  IsBound and Unbind for Records, \indexit{258}
  `IsBoundGlobal', 44
  `IsBrauerTable', 713
  `IsBravaisGroup', 424
  `IsBuiltFromAdditiveMagmaWithInverses', 338
  `IsBuiltFromGroup', 338
  `IsBuiltFromMagma', 338
  `IsBuiltFromMagmaWithInverses', 338
  `IsBuiltFromMagmaWithOne', 338
  `IsBuiltFromSemigroup', 338
  `IsCanonicalBasis', 590
  `IsCanonicalBasisFullMatrixModule', 594
  `IsCanonicalBasisFullRowModule', 594
  `IsCanonicalNiceMonomorphism', 380
  `IsCanonicalPcgs', 432
  `IsCentral', 316
  `IsChar', 242
  `IsCharacter', 759
  `IsCharacteristicSubgroup', 343
  `IsCharacterTable', 713
  `IsCharacterTableInProgress', 713
  `IsCharCollection', 242
  `IsClassFunction', 750
  `IsClassFusionOfNormalSubgroup', 729
  `IsClosedStream', 96
  `IsCochain', 640
  `IsCochainCollection', 640
  `IsCollection', 260
  `IsCollectionFamily', 260
  `IsCommutative', 316
  `IsCommutativeElement', 294
  `IsCommutativeElementCollColl', 294
  `IsCommutativeElementCollection', 294
  `IsCompositionMappingRep', 297
  `IsConfluent', 336
    \sub for pc groups, 446
  `Is\-Conjugacy\-Class\-Subgroups\-By\-Stabilizer\-Rep', 363
  `IsConjugacyClassSubgroupsRep', 363
  `IsConjugate', 351
  `IsConjugatorAutomorphism', 381
  `IsConjugatorIsomorphism', 381
  `IsConstantRationalFunction', 658
  `IsConstantTimeAccessGeneralMapping', 305
  `IsConstantTimeAccessList', 169
  `IsContainedInSpan', 592
  `IsCopyable', 111
  `IsCyc', 153
  `IsCyclic', 356
    \sub for character tables, 720
  `IsCyclicTom', 697
  `IsCyclotomic', 153
  `IsCyclotomicField', 579
  `IsCyclotomicMatrixGroup', 423
  `IsDenseList', 168
  `IsDiagonalMat', 219
  `IsDigitChar', 246
  `IsDirectoryPath', 92
  `IsDistributive', 556
  `IsDivisionRing', 566
  `IsDomain', 284
  `IsDoneIterator', 271
  `IsDoubleCoset', 349
  `IsDuplicateFree', 188
  `IsDuplicateFreeList', 188
  `IsDxLargeGroup', 738
  `IsElementaryAbelian', 356
  `IsElementOfFpMonoid', 538
  `IsElementOfFpSemigroup', 538
  `IsElementOfFreeMagmaRing', 649
  `IsElementOfFreeMagmaRingCollection', 649
  `IsElementOfFreeMagmaRingFamily', 649
  `IsElementOfMagmaRingModuloRelations', 651
  `Is\-Element\-Of\-Magma\-Ring\-Modulo\-Relations\-Collection', 651
  `Is\-Element\-Of\-Magma\-Ring\-Modulo\-Relations\-Family', 651
  `Is\-Element\-Of\-Magma\-Ring\-Modulo\-Span\-Of\-Zero\-Family', 651
  `IsEmpty', 265
  `IsEmptyString', 245
  `IsEndOfStream', 99
  `IsEndoGeneralMapping', 305
    \sub same as `IsBinaryRelation', 307
  `IsEqualSet', 191
  `IsEquivalenceClass', 310
  `IsEquivalenceRelation', 308
  `IsEuclideanRing', 558
  `IsEvenInt', 126
  `IsExecutableFile', 92
  `IsExistingFile', 92
  `IsExtAElement', 292
  `IsExternalOrbit', 400
  `IsExternalSet', 399
  `IsExternalSubset', 400
  `IsExtLElement', 292
  `IsExtRElement', 292
  `IsFamilyPcgs', 443
  `IsFFE', 572
  `IsFFECollColl', 572
  `IsFFECollection', 572
  `IsField', 566
  `IsFieldControlledByGaloisGroup', 569
  `IsFieldHomomorphism', 305
  `IsFinite', 265
    \sub for character tables, 720
  `IsFiniteDimensional', 564
    \sub for matrix algebras, 608
  `IsFiniteFieldPolynomialRing', 667
  `IsFinitelyGeneratedGroup', 357
  `IsFiniteOrderElement', 294
  `IsFiniteOrderElementCollColl', 294
  `IsFiniteOrderElementCollection', 294
  `IsFiniteOrdersPcgs', 428
  `IsFixedStabilizer', 416
  `IsFLMLOR', 607
  `IsFLMLORWithOne', 607
  `IsFpGroup', 454
  `IsFpMonoid', 538
  `IsFpSemigroup', 537
  `IsFreeGroup', 324
  `IsFreeLeftModule', 563
  `IsFreeMagmaRing', 649
  `IsFreeMagmaRingWithOne', 649
  `IsFromFpGroupGeneralMappingByImages', 386
  `IsFromFpGroupHomomorphismByImages', 386
  `Is\-From\-Fp\-Group\-Std\-Gens\-General\-Mapping\-By\-Images', 386
  `Is\-From\-Fp\-Group\-Std\-Gens\-Homomorphism\-By\-Images', 386
  `IsFullHomModule', 597
  `IsFullMatrixModule', 565
  `IsFullRowModule', 565
  `Is\-Full\-Subgroup\-GLor\-SLRespecting\-Bilinear\-Form', 422
  `Is\-Full\-Subgroup\-GLor\-SLRespecting\-Quadratic\-Form', 423
  `Is\-Full\-Subgroup\-GLor\-SLRespecting\-Sesquilinear\-Form', 422
  `IsFullTransformationSemigroup', 529
  `IsFunction', 62
  `IsGaussianIntegers', 583
  `IsGaussianRationals', 578
  `IsGaussianSpace', 592
  `IsGaussInt', 156
  `IsGaussRat', 156
  `IsGeneralizedDomain', 284
  `IsGeneralizedRowVector', 179
  `IsGeneralLinearGroup', 421
  `IsGeneralMapping', 305
  `IsGeneralMappingFamily', 306
  `IsGeneratorsOf<Struct>', 281
  `IsGL', 421
  `IsGreensClass', 531
  `IsGreensDClass', 531
  `IsGreensDRelation', 530
  `IsGreensHClass', 531
  `IsGreensHRelation', 530
  `IsGreensJClass', 531
  `IsGreensJRelation', 530
  `IsGreensLClass', 531
  `IsGreensLessThanOrEqual', 531
  `IsGreensLRelation', 530
  `IsGreensRClass', 531
  `IsGreensRelation', 530
  `IsGreensRRelation', 530
  `IsGroup', 342
  `IsGroupGeneralMapping', 303
  `Is\-Group\-General\-Mapping\-By\-As\-Group\-General\-Mapping\-By\-Images', 385
  `IsGroupGeneralMappingByImages', 385
  `IsGroupGeneralMappingByPcgs', 386
  `IsGroupHClass', 532
  `IsGroupHomomorphism', 303
  `IsGroupOfAutomorphisms', 382
  `IsGroupRing', 649
  `IsHandledByNiceBasis', 565
    \sub for vector spaces, 598
  `IsHandledByNiceMonomorphism', 380
  `IsHasseDiagram', 308
  `IsHomogeneousList', 169
  `IsIdempotent', 287
  `IsIdenticalObj', 110
  `IsIncomparableUnder', 274
  `IsInducedFromNormalSubgroup', 809
  `IsInducedPcgs', 431
  `IsInducedPcgsWrtSpecialPcgs', 439
  `IsInfBitsFamily', 330
  `IsInfinity', 156
  `IsInjective', 298
  `IsInnerAutomorphism', 381
  `IsInputOutputStream', 103
  `IsInputStream', 96
  `IsInputTextNone', 96
  `IsInputTextStream', 96
  `IsInt', 125
  `IsIntegerMatrixGroup', 423
  `IsIntegers', 125
  `IsIntegralBasis', 590
  `IsIntegralCyclotomic', 154
  `IsIntegralRing', 555
  `IsInternallyConsistent', 114
    \sub for character tables, 728
    \sub for tables of marks, 697
  `IsIrreducibleCharacter', 759
  `IsIrreducibleRingElement', 557
  `IsIterator', 271
  `IsJacobianElement', 294
  `IsJacobianElementCollColl', 294
  `IsJacobianElementCollection', 294
  `IsJacobianRing', 556
  `IsLaurentPolynomial', 658
  `IsLaurentPolynomialDefaultRep', 674
  `IsLDistributive', 555
  `IsLeftAlgebraModuleElement', 619
  `IsLeftAlgebraModuleElementCollection', 619
  `IsLeftIdeal', 553
  `IsLeftIdealInParent', 553
  `IsLeftModule', 562
  `IsLeftModuleGeneralMapping', 304
  `IsLeftModuleHomomorphism', 304
  `IsLeftOperatorAdditiveGroup', 562
  `IsLeftSemigroupIdeal', 529
  `IsLeftVectorSpace', 584
  `IsLessThanOrEqualUnder', 274
  `IsLessThanUnder', 274
  `IsLetterAssocWordRep', 329
  `IsLetterWordsFamily', 329
  `IsLexicographicallyLess', 194
  `IsLieAbelian', 630
  `IsLieAlgebra', 607
  `IsLieMatrix', 216
  `IsLieNilpotent', 630
  `IsLieObject', 625
  `IsLieObjectCollection', 625
  `IsLieSolvable', 630
  `IsLinearMapping', 304
  `IsLinearMappingsModule', 597
  `IsList', 168
  `IsListDefault', 179
  `IsListOrCollection', 261
  `IsLowerAlphaChar', 246
  `IsLowerTriangularMat', 219
  `IsMagma', 312
  `IsMagmaHomomorphism', 302
  `IsMagmaRingModuloRelations', 651
  `IsMagmaRingModuloSpanOfZero', 651
  `IsMagmaWithInverses', 312
  `IsMagmaWithInversesIfNonzero', 312
  `IsMagmaWithOne', 312
  `IsMapping', 298
  `IsMatchingSublist', 188
  `IsMatrix', 215
  `IsMatrixGroup', 420
  `IsMatrixModule', 565
  `IsMatrixSpace', 592
  `IsMinimalNonmonomial', 812
  `IsModuloPcgs', 433
  `IsMonoid', 534
  `IsMonomial', for characters, 809
    \sub for character tables, 720
    \sub for groups, 809
    \sub for positive integers, 810
  `IsMonomialGroup', 357
  `IsMonomialMatrix', 219
  `IsMonomialNumber', 810
  `IsMonomialOrdering', 667
  `IsMultiplicativeElement', 292
  `IsMultiplicativeElementWithInverse', 293
  `IsMultiplicativeElementWithOne', 292
  `IsMultiplicativeElementWithZero', 292
  `IsMultiplicativeGeneralizedRowVector', 179
  `IsMultiplicativeZero', 316
  `IsMutable', 112
  `IsMutableBasis', 591
  `IsNaturalAlternatingGroup', 407
  `IsNaturalGL', 421
  `IsNaturalGLnZ', 423
  `IsNaturalSL', 422
  `IsNaturalSLnZ', 424
  `IsNaturalSymmetricGroup', 407
  `IsNearAdditiveElement', 292
  `IsNearAdditiveElementWithInverse', 292
  `IsNearAdditiveElementWithZero', 292
  `IsNearAdditiveGroup', 546
  `IsNearAdditiveMagma', 546
  `IsNearAdditiveMagmaWithInverses', 546
  `IsNearAdditiveMagmaWithZero', 546
  `IsNearlyCharacterTable', 713
  `IsNearRingElement', 293
  `IsNearRingElementWithInverse', 293
  `IsNearRingElementWithOne', 293
  `IsNegRat', 142
  `IsNilpotent', for character tables, 720
    \sub for groups with pcgs, 441
  `IsNilpotentElement', 637
  `IsNilpotentGroup', 356
  `IsNilpotentTom', 697
  `IsNonassocWord', 319
  `IsNonassocWordCollection', 319
  `IsNonassocWordWithOne', 319
  `IsNonassocWordWithOneCollection', 319
  `IsNonnegativeIntegers', 125
  `IsNonSPGeneralMapping', 306
  `IsNonTrivial', 265
  `IsNormal', 343
  `IsNormalBasis', 590
  `IsNotIdenticalObj', 111
  `IsNumberField', 578
  `IsObject', 109
  `IsOddInt', 126
  isomorphic, pc group, 447
  `IsomorphicSubgroups', 384
  `IsomorphismFpAlgebra', 616
  `IsomorphismFpGroup', 462
    \sub for subgroups of fp groups, 465
  `IsomorphismFpGroupByGenerators', 463
  `IsomorphismFpGroupByGeneratorsNC', 463
  `IsomorphismFpGroupByPcgs', 445
  `IsomorphismFpSemigroup', 538
  `IsomorphismGroups', 383
  `IsomorphismMatrixAlgebra', 616
  `IsomorphismPcGroup', 447
  `IsomorphismPermGroup', 406
    \sub for Imf matrix groups, 525
  `IsomorphismPermGroupImfGroup', 526
  `IsomorphismReesMatrixSemigroup', 533
  `IsomorphismRefinedPcGroup', 447
  `Isomorphism<Rep><Struct>', 282
  isomorphisms, find all, 384
  `IsomorphismSCAlgebra', 617
  `IsomorphismSimplifiedFpGroup', 465
  `IsomorphismSpecialPcGroup', 448
  `IsomorphismTransformationSemigroup', 529
  `IsomorphismTypeInfoFiniteSimpleGroup', 357
  `IsOne', 287
  `IsOperation', 62
  `IsOrdering', 273
  `IsOrderingOnFamilyOfAssocWords', 274
  `IsOrdinaryMatrix', 215
  `IsOrdinaryTable', 713
  `IsOutputStream', 96
  `IsOutputTextNone', 97
  `IsOutputTextStream', 96
  `IsPadicExtensionNumber', 680
  `IsPadicExtensionNumberFamily', 680
  `IsParentPcgsFamilyPcgs', 443
  `IsPartialOrderBinaryRelation', 308
  `IsPcGroup', 444
  `IsPcGroupGeneralMappingByImages', 386
  `IsPcGroupHomomorphismByImages', 386
  `IsPcgs', 427
  `IsPcgsCentralSeries', 435
  `IsPcgsChiefSeries', 436
  `IsPcgsElementaryAbelianSeries', 435
  `IsPcgsPCentralSeriesPGroup', 436
  `IsPerfect', for character tables, 720
  `IsPerfectGroup', 356
  `IsPerfectTom', 697
  `IsPerm', 402
  `IsPermCollColl', 402
  `IsPermCollection', 402
  `IsPermGroup', 406
  `IsPermGroupGeneralMappingByImages', 386
  `IsPermGroupHomomorphismByImages', 386
  `IsPGroup', 358
  `IsPNilpotent', 358
  `IsPolycyclicGroup', 356
  `IsPolynomial', 658
  `IsPolynomialDefaultRep', 674
  `IsPolynomialFunction', 657
  `IsPolynomialFunctionsFamily', 672
  `IsPolynomialRing', 666
  `IsPosInt', 125
  `IsPositiveIntegers', 125
  `IsPosRat', 141
  `Is\-Preimages\-By\-As\-Group\-General\-Mapping\-By\-Images', 386
  `IsPreOrderBinaryRelation', 308
  `IsPrime', 557
  `IsPrimeField', 568
  `IsPrimeInt', 130
  `IsPrimeOrdersPcgs', 428
  `IsPrimePowerInt', 131
  `IsPrimitive', 397
  `IsPrimitiveCharacter', 808
  `IsPrimitivePolynomial', 659
  `IsPrimitiveRootMod', 136
  `IsProbablyPrimeInt', 130
  `IsPseudoCanonicalBasisFullHomModule', 597
  `IsPSolvable', 358
  `IsPSolvableCharacterTable', 729
  `IsPSolvableCharacterTableOp', 729
  `IsPurePadicNumber', 679
  `IsPurePadicNumberFamily', 679
  `IsQuasiPrimitive', 808
  `IsQuaternion', 608
  `IsQuaternionCollColl', 608
  `IsQuaternionCollection', 608
  `IsQuickPositionList', 203
  `IsQuotientSemigroup', 530
  `IsRange', 202
  `IsRat', 141
  `IsRationalFunction', 657
  `IsRationalFunctionDefaultRep', 673
  `IsRationalFunctionsFamily', 672
  `IsRationalMatrixGroup', 423
  `IsRationals', 141
  `IsRationalsPolynomialRing', 667
  `IsRDistributive', 556
  `IsReadableFile', 92
  `IsReadOnlyGlobal', 43
  `IsRecord', 254
  `IsRecordCollColl', 254
  `IsRecordCollection', 254
  `IsReduced', 337
  `IsReductionOrdering', 275
  `IsReesCongruence', 530
  `IsReesCongruenceSemigroup', 528
  `IsReesMatrixSemigroup', 532
  `IsReesMatrixSemigroupElement', 532
  `IsReesZeroMatrixSemigroup', 532
  `IsReesZeroMatrixSemigroupElement', 532
  `IsReflexiveBinaryRelation', 307
  `IsRegular', 397
  `IsRegularDClass', 532
  `IsRegularSemigroup', 528
  `IsRegularSemigroupElement', 528
  `IsRelativelySM', 811
  `IsRestrictedLieAlgebra', 635
  `IsRewritingSystem', 336
  `IsRightAlgebraModuleElement', 619
  `IsRightAlgebraModuleElementCollection', 619
  `IsRightCoset', 347
  `IsRightIdeal', 553
  `IsRightIdealInParent', 553
  `IsRightModule', 562
  `IsRightOperatorAdditiveGroup', 562
  `IsRightSemigroupIdeal', 529
  `IsRing', 550
  `IsRingElement', 293
  `IsRingElementWithInverse', 293
  `IsRingElementWithOne', 293
  `IsRingGeneralMapping', 305
  `IsRingHomomorphism', 305
  `IsRingWithOne', 554
  `IsRingWithOneGeneralMapping', 305
  `IsRingWithOneHomomorphism', 305
  `IsRootSystem', 631
  `IsRootSystemFromLieAlgebra', 632
  `IsRowModule', 565
  `IsRowSpace', 592
  `IsRowVector', 208
  `IsScalar', 293
  `IsSemiEchelonized', 593
  `IsSemigroup', 527
  `IsSemigroupCongruence', 529
  `IsSemigroupIdeal', 529
  `IsSemiRegular', 397
  `IsSet', 189
  `IsShortLexLessThanOrEqual', 326
  `IsShortLexOrdering', 276
  `IsSimple', for character tables, 720
  `IsSimpleAlgebra', 607
  `IsSimpleGroup', 357
  `IsSimpleSemigroup', 528
  `IsSingleValued', 298
  `IsSL', 421
  `IsSolvable', for character tables, 720
  `IsSolvableGroup', 356
  `IsSolvableTom', 697
  `IsSortedList', 188
  `IsSpecialLinearGroup', 421
  `IsSpecialPcgs', 438
  `IsSPGeneralMapping', 306
  `IsSporadicSimple', for character tables, 720
  `IsSSortedList', 189
  `IsStandardGeneratorsOfGroup', 702
  `IsStraightLineProgElm', 335
  `IsStraightLineProgram', 331
  `IsStream', 96
  `IsString', 242
  `IsStringRep', 245
  `Is<Struct>', 282
  `IsSubgroup', 343
  `IsSubgroupFpGroup', 454
  `IsSubgroupOfWholeGroupByQuotientRep', 466
  `IsSubgroupSL', 422
  `IsSubmonoidFpMonoid', 537
  `IsSubnormal', 344
  `IsSubnormallyMonomial', 811
  `IsSubsemigroupFpSemigroup', 537
  `IsSubset', 267
  `IsSubsetBlist', 205
  `IsSubsetLocallyFiniteGroup', 357
  `IsSubsetSet', 191
  `IsSubspacesVectorSpace', 585
  `IsSub<struct>', 284
  `IsSupersolvable', for character tables, 720
    \sub for groups with pcgs, 441
  `IsSupersolvableGroup', 356
  `IsSurjective', 299
  `IsSyllableAssocWordRep', 330
  `IsSyllableWordsFamily', 330
  `IsSymmetricBinaryRelation', 307
  `IsSymmetricGroup', 408
  `IsTable', 169
  `IsTableOfMarks', 693
  `IsTableOfMarksWithGens', 704
  `IsToPcGroupGeneralMappingByImages', 386
  `IsToPcGroupHomomorphismByImages', 386
  `IsToPermGroupGeneralMappingByImages', 386
  `IsToPermGroupHomomorphismByImages', 386
  `IsTotal', 298
  `IsTotalOrdering', 274
  `IsTransformation', 543
  `IsTransformationCollection', 543
  `IsTransformationMonoid', 529
  `IsTransformationSemigroup', 529
  `IsTransitive', for characters, 762
    \sub for class functions, 762
    \sub for group actions, 396
  `IsTransitiveBinaryRelation', 307
  `IsTranslationInvariantOrdering', 274
  `IsTrivial', 265
  `IsTuple', 296
  `IsTwoSidedIdeal', 553
  `IsTwoSidedIdealInParent', 553
  `IsUEALatticeElement', 643
  `IsUEALatticeElementCollection', 643
  `IsUEALatticeElementFamily', 643
  `IsUniqueFactorizationRing', 555
  `IsUnit', 556
  `IsUnivariatePolynomial', 658
  `IsUnivariatePolynomialRing', 667
  `IsUnivariateRationalFunction', 658
  `IsUnknown', 163
  `IsUpperAlphaChar', 246
  `IsUpperTriangularMat', 219
  `IsValidIdentifier', 41
  `IsVector', 293
  `IsVectorSpace', 584
  `IsVirtualCharacter', 759
  `IsWeightLexOrdering', 277
  `IsWeightRepElement', 644
  `IsWeightRepElementCollection', 644
  `IsWeightRepElementFamily', 644
  `IsWellFoundedOrdering', 273
  `IsWeylGroup', 633
  `IsWholeFamily', 266
  `IsWLetterAssocWordRep', 329
  `IsWLetterWordsFamily', 329
  `IsWord', 318
  `IsWordCollection', 319
  `IsWordWithInverse', 318
  `IsWordWithOne', 318
  `IsWreathProductOrdering', 278
  `IsWritableFile', 92
  `IsZero', 287
  `IsZeroGroup', 528
  `IsZeroSimpleSemigroup', 528
  `IsZeroSquaredElement', 294
  `IsZeroSquaredElementCollColl', 294
  `IsZeroSquaredElementCollection', 294
  `IsZeroSquaredRing', 556
  `IsZmodnZObj', 133
  `IsZmodnZObjNonprime', 133
  `IsZmodpZObj', 133
  `IsZmodpZObjLarge', 133
  `IsZmodpZObjSmall', 133
  `Iterated', 199
  `Iterator', 270
  `IteratorByBasis', 589
  `IteratorByFunctions', 272
  `IteratorList', 271
  Iterators, \indexit{270}
  `IteratorSorted', 271
\letter J
  $j_N$, 158
  `Jacobi', 136
  `JenningsLieAlgebra', 636
  `JenningsSeries', 361
  `JoinEquivalenceRelations', 310
  `JoinStringsWithSeparator', 248
  `JordanDecomposition', 227
\letter K
  $k_N$, 158
  `KappaPerp', 637
  `KB_REW', 541
  `KernelOfAdditiveGeneralMapping', 304
  `KernelOfCharacter', 761
  `KernelOfMultiplicativeGeneralMapping', 303
  `KernelOfTransformation', 544
  Keywords, \indexit{40}
  `KillingMatrix', 637
  `KnownAttributesOfObject', 120
  Known Problems of the Configure Process, \indexit{820}
  `KnownPropertiesOfObject', 123
  `KnownTruePropertiesOfObject', 123
  `KnowsHowToDecompose', 374
  `KnuthBendixRewritingSystem', 541
  Krasner-Kaloujnine theorem, 498
  `KroneckerProduct', 221
  `KuKGenerators', 498
\letter L
  $l_N$, 158
  `Lambda', 134
  Language Overview, \indexit{38}
  larger or equal, 46
  larger test, 46
  `LargestElementGroup', 370
  `LargestElementStabChain', 415
  `LargestMovedPoint', 403
  `LargestUnknown', 163
  `last', 63
  `LastSystemError', 89
  `LaTeXStringDecompositionMatrix', 727
  lattice base reduction, 238, 239
  lattice basis reduction, for virtual characters, 766
  `LatticeByCyclicExtension', 367
  `LatticeGeneratorsInUEA', 643
  Lattice Reduction, \indexit{238}
  `LatticeSubgroups', 365
  `LatticeSubgroupsByTom', 690
  `LaurentPolynomialByCoefficients', 664
  `LaurentPolynomialByExtRep', 675
  Laurent Polynomials, \indexit{664}
  `LClassOfHClass', 531
  `Lcm', 560
  `LcmInt', 129
  `LcmOp', 560
  `LeadCoeffsIGS', 432
  `LeadingCoefficient', 660
  `LeadingCoefficientOfPolynomial', 668
  `LeadingExponentOfPcElement', 429
  `LeadingMonomial', 660
  `LeadingMonomialOfPolynomial', 668
  `LeadingTermOfPolynomial', 668
  Leaving GAP, \indexit{71}
  `LeftActingAlgebra', 620
  `LeftActingDomain', 563
  `LeftActingRingOfIdeal', 554
  `LeftAlgebraModule', 618
  `LeftAlgebraModuleByGenerators', 617
  left cosets, 347
  `LeftDerivations', 627
  `LeftIdeal', 552
  `LeftIdealByGenerators', 553
  `LeftIdealNC', 553
  `LeftModuleByGenerators', 563
  `LeftModuleByHomomorphismToMatAlg', 621
  `LeftModuleGeneralMappingByImages', 595
  `LeftModuleHomomorphismByImages', 595
  `LeftModuleHomomorphismByImagesNC', 595
  `LeftModuleHomomorphismByMatrix', 596
  `LeftQuotient', 289
    \sub for words, 326
  `LeftShiftRowVector', 212
  legacy, 832
  `Legendre', 137
  `Length', 189
    \sub of an associative word, 327
  length, of a word, 327
  `LengthsTom', 694
  `LenstraBase', 581
  `LessThanFunction', 274
  `LessThanOrEqualFunction', 274
  `LetterRepAssocWord', 330
  `LevelsOfGenerators', 278
  `LeviMalcevDecomposition', 613
    \sub for Lie algebras, 631
  Lexical Structure, \indexit{39}
  `LexicographicOrdering', 275
  `LGFirst', 439
  `LGLayers', 438
  `LGLength', 439
  `LGWeights', 438
  library tables, 711
  `LieAlgebra', 626
  `LieAlgebraByStructureConstants', 626
  `LieBracket', 289
  `LieCenter', 628
  `LieCentralizer', 628
  `LieCentre', 628
  `LieCoboundaryOperator', 641
  `LieDerivedSeries', 629
  `LieDerivedSubalgebra', 628
  `LieFamily', 625
  `LieLowerCentralSeries', 629
  `LieNilRadical', 629
  `LieNormalizer', 628
  `LieObject', 625
  Lie objects, \indexit{625}
  `LieSolvableRadical', 629
  `LieUpperCentralSeries', 630
  `LiftedInducedPcgs', 434
  `LiftedPcElement', 434
  `LinearAction', 440
  `LinearActionLayer', 440
  `LinearCharacters', 719
  `LinearCombination', 589
  `LinearCombinationPcgs', 429
  Linear equations over the integers and Integral Matrices, \indexit{233}
  `LinearIndependentColumns', 237
  Linear Mappings, \indexit{304}
  `LinearOperation', 440
  `LinearOperationLayer', 440
  Line Editing, \indexit{72}
  `LinesOfStraightLineProgram', 332
  `List', 196
  list and non-list, difference, 181
    \sub left quotient, 184
    \sub mod, 183
    \sub product, 182
    \sub quotient, 183
  List Assignment, \indexit{171}
  list assignment, operation, 170
  `ListBlist', 204
  list boundedness test, operation, 170
  List Categories, \indexit{168}
  list element, access, 170
    \sub assignment, 171
    \sub operation, 170
  List Elements, \indexit{170}
  list equal, comparison, 177
  `ListN', 199
  list of available books, 23
  `ListPerm', 404
  Lists and Collections, \indexit{261}
  list smaller, comparison, 178
  `ListStabChain', 415
  list unbind, operation, 170
  `ListWithIdenticalEntries', 185
  `ListX', 200
  `LLL', 766
  LLL algorithm, for Gram matrices, 239
    \sub for vectors, 238
    \sub for virtual characters, 766
  `LLLReducedBasis', 238
  `LLLReducedGramMat', 239
  `LoadDynamicModule', 35
  Loading a GAP Package, \indexit{828}
  loading a saved workspace, 37
  `LoadPackage', 828
  `local', 54
  logarithm, discrete, 135
    \sub of a root of unity, 156
  `LogFFE', 574
  logical, 165
  logical operations, 166
  `LogInt', 127
  `LogMod', 135
  `LogModShanks', 135
  `LogTo', 94
    \sub for streams, 101
    \sub stop logging, 94
  `LongestWeylWordPerm', 634
  loop, read eval print, 63
  loop, `for', 51
    \sub `repeat', 51
    \sub `while', 50
  loop over iterator, 53
  loop over object, 53
  loop over range, 52
  loops, leaving, 53
    \sub restarting, 54
  `LowercaseString', 247
  `LowerCentralSeriesOfGroup', 361
  Low Index Subgroups, \indexit{461}
  `LowIndexSubgroupsFpGroup', 461
  Low Level Routines to Modify and Create Stabilizer Chains, \indexit{415}
  `Lucas', 151
\letter M
  $m_N$, 158
  Macintosh, 822, 823
  MacOS, 823
  `Magma', 312
  `MagmaByGenerators', 313
  `MagmaByMultiplicationTable', 314
  Magma Categories, \indexit{312}
  `MagmaElement', 314
  Magma Generation, \indexit{312}
  `MagmaHomomorphismByFunctionNC', 302
  Magma Homomorphisms, \indexit{302}
  `MagmaRingModuloSpanOfZero', 651
  Magma Rings modulo Relations, \indexit{651}
  Magma Rings modulo the Span of a Zero Element, \indexit{651}
  Magmas Defined by Multiplication Tables, \indexit{314}
  `MagmaWithInverses', 313
  `MagmaWithInversesByGenerators', 313
  `MagmaWithInversesByMultiplicationTable', 314
  `MagmaWithOne', 312
  `MagmaWithOneByGenerators', 313
  `MagmaWithOneByMultiplicationTable', 314
  Main Loop, \indexit{63}
  `MakeConfluent', 337
  `MakeImmutable', 112
  `MakeReadOnlyGlobal', 43
  `MakeReadWriteGlobal', 43
  Making transformation semigroups, \indexit{529}
  Manual Conventions, \indexit{20}
  map, parametrized, 793
  `MappedWord', 320
  `MappingByFunction', 296
  `MappingPermListList', 405
  Mappings that Respect Addition, \indexit{303}
  Mappings that Respect Multiplication, \indexit{302}
  Mappings which are Compatible with Algebraic Structures, \indexit{302}
  maps, 784
  `MarksTom', 693
  `MatAlgebra', 604
  `MatClassMultCoeffsCharTable', 731
  `MathieuGroup', 501
  `MatLieAlgebra', 627
  matrices, commutator, 217
  Matrices as Basis of a Row Space, \indexit{225}
  Matrices as Linear Mappings, \indexit{227}
  Matrices over Finite Fields, \indexit{228}
  Matrices Representing Linear Equations and the Gaussian Algorithm, \indexit{222}
  `MatrixAlgebra', 604
  `MatrixAutomorphisms', 745
  matrix automorphisms, 787
  `MatrixByBlockMatrix', 232
  Matrix Constructions, \indexit{219}
  Matrix Groups in Characteristic 0, \indexit{423}
  `MatrixLieAlgebra', 627
  `MatrixOfAction', 620
  matrix spaces, 592
  `MatScalarProducts', 760
  `MatTom', 696
  `MaximalAbelianQuotient', 363
  `MaximalBlocks', 398
  `MaximalNormalSubgroups', 364
  `MaximalSubgroupClassReps', 364
  `MaximalSubgroups', 364
    \sub for groups with pcgs, 441
  `MaximalSubgroupsLattice', 365
  `MaximalSubgroupsTom', 700
  `Maximum', 195
  `MaximumList', 195
  MeatAxe Modules, \indexit{682}
  `MeetEquivalenceRelations', 310
  `MeetMaps', 796
  Membership Test for Collections, \indexit{268}
  Membership Test for Lists, \indexit{177}
  `MinimalElementCosetStabChain', 415
  `MinimalGeneratingSet', 370
    \sub for groups with pcgs, 441
  `MinimalNonmonomialGroup', 812
  Minimal Nonmonomial Groups, \indexit{812}
  `MinimalNormalSubgroups', 365
  `MinimalPolynomial', 662
    \sub over a field, 569
    \sub over a ring, 662
  Minimal Polynomials, \indexit{662}
  `MinimalStabChain', 413
  `MinimalSupergroupsLattice', 366
  `MinimalSupergroupsTom', 700
  `MinimizedBombieriNorm', 664
  `Minimum', 195
  `MinimumList', 195
  `MinusCharacter', 802
  Miscellaneous, \indexit{139}
  Miscellaneous Name Changes or Removed Names, \indexit{833}
  mod, integers, 133
    \sub laurent polynomials, 656
    \sub lists, 183
    \sub rationals, 47
  `mod', 47
    \sub arithmetic operators, 47
    \sub for character tables, 717
    \sub residue class rings, 132
  modular inverse, 47
  modular remainder, 47
  modular roots, 138
  `ModuleByRestriction', 622
  Module Constructions, \indexit{682}
  Module Homomorphisms, \indexit{684}
  `ModuleOfExtension', 449
  Modules over Lie Algebras and Their Cohomology, \indexit{640}
  Modules over Semisimple Lie Algebras, \indexit{642}
  modulo, 47
    \sub arithmetic operators, 47
    \sub for pcgs, 433
    \sub residue class rings, 132
  `ModuloPcgs', 433
  `MoebiusMu', 139
  `MoebiusTom', 696
  Molien Series, \indexit{773}
  `MolienSeries', 773
  `MolienSeriesInfo', 774
  `MolienSeriesWithGivenDenominator', 775
  `Monoid', 534
  `MonoidByGenerators', 534
  `MonoidByMultiplicationTable', 535
  `MonoidOfRewritingSystem', 542
  `MonomialComparisonFunction', 668
  `MonomialExtGrlexLess', 670
  `MonomialExtrepComparisonFun', 669
  `MonomialGrevlexOrdering', 669
  `MonomialGrlexOrdering', 669
  `MonomialLexOrdering', 669
  Monomial Orderings, \indexit{667}
  `MonomialTotalDegreeLess', 833
  monomorphisms, find all, 384
  `MorClassLoop', 384
  More about Boolean Lists, \indexit{206}
  More About Global Variables, \indexit{43}
  More about Tables of Marks, \indexit{688}
  `MostFrequentGeneratorFpGroup', 460
  `MovedPoints', 403
  Moved Points of Permutations, \indexit{403}
  `MTX.BasesCompositionSeries', 684
  `MTX.BasesMaximalSubmodules', 683
  `MTX.BasesMinimalSubmodules', 683
  `MTX.BasesMinimalSupermodules', 684
  `MTX.BasesSubmodules', 683
  `MTX.BasisInOrbit', 685
  `MTX.BasisRadical', 683
  `MTX.BasisSocle', 683
  `MTX.CollectedFactors', 684
  `MTX.CompositionFactors', 684
  `MTX.DegreeSplittingField', 683
  `MTX.Dimension', 683
  `MTX.Distinguish', 685
  `MTX.Field', 683
  `MTX.Generators', 683
  `MTX.Homomorphism', 685
  `MTX.Homomorphisms', 685
  `MTX.InducedAction', 684
  `MTX.InducedActionFactorMatrix', 684
  `MTX.InducedActionFactorModule', 684
  `MTX.InducedActionMatrix', 684
  `MTX.InducedActionMatrixNB', 684
  `MTX.InducedActionSubmodule', 684
  `MTX.InducedActionSubmoduleNB', 684
  `MTX.InvariantBilinearForm', 685
  `MTX.InvariantQuadraticForm', 685
  `MTX.InvariantSesquilinearForm', 685
  `MTX.IsAbsolutelyIrreducible', 683
  `MTX.IsEquivalent', 684
  `MTX.IsIrreducible', 683
  `MTX.Isomorphism', 685
  `MTX.NormedBasisAndBaseChange', 684
  `MTX.OrthogonalSign', 685
  `MTX.ProperSubmoduleBasis', 683
  `MTX.SubGModule', 683
  `MTX.SubmoduleGModule', 683
  multiplication, 47
    \sub matrices, 217
    \sub matrix and matrix list, 218
    \sub matrix and scalar, 216
    \sub matrix and vector, 217
    \sub operation, 289
    \sub scalar and matrix, 216
    \sub scalar and matrix list, 217
    \sub scalar and vector, 209
    \sub vector and matrix, 216
    \sub vector and matrix list, 218
    \sub vector and scalar, 209
    \sub vectors, 209
  `MultiplicationTable', 314
  Multiplicative Arithmetic for Lists, \indexit{182}
  Multiplicative Arithmetic Functions, \indexit{138}
  `MultiplicativeNeutralElement', 316
  multiplicative order of an integer, 135
  `MultiplicativeZero', 316
  `MultiplicativeZeroOp', 286
  multiplicity, of constituents of a group character, 760
  multiplier, 373
  multisets, 190
  Multivariate Polynomials, \indexit{661}
  `MultRowVector', 212
  Murnaghan components, 772, 773
  Mutability and Copyability, \indexit{111}
  Mutability Status and List Arithmetic, \indexit{184}
  Mutable Bases, \indexit{590}
  `MutableBasis', 591
  `MutableBasisOfClosureUnderAction', 610
  `Mutable\-Basis\-Of\-Ideal\-In\-Nonassociative\-Algebra', 611
  `MutableBasisOfNonassociativeAlgebra', 611
  `MutableIdentityMat', 221
  `MutableNullMat', 221
\letter N
  $n_k$, 158
  `Name', 114
  `NameFunction', 60
  `NameRNam', 259
  `NamesFilter', 117
  `NamesGVars', 44
  `NamesOfFusionSources', 791
  `NamesSystemGVars', 44
  `NamesUserGVars', 44
  `NaturalCharacter', 758
  Natural Embeddings related to Magma Rings, \indexit{650}
  `NaturalHomomorphismByGenerators', 302
  `NaturalHomomorphismByIdeal', 615
  `NaturalHomomorphismByNormalSubgroup', 362
  `NaturalHomomorphismByNormalSubgroupNC', 362
  `NaturalHomomorphismBySubAlgebraModule', 622
  `NaturalHomomorphismBySubspace', 596
  `NearAdditiveGroup', 547
  `NearAdditiveGroupByGenerators', 547
  `NearAdditiveMagma', 547
  `NearAdditiveMagmaByGenerators', 547
  `NearAdditiveMagmaWithZero', 547
  `NearAdditiveMagmaWithZeroByGenerators', 547
  `NearlyCharacterTablesFamily', 715
  negative number, 47
  `NegativeRoots', 632
  `NegativeRootVectors', 632
  `NestingDepthA', 180
  `NestingDepthM', 180
  `NewInfoClass', 78
  newline, 39
  newline character, 244
  `NewmanInfinityCriterion', 470
  New Presentations and Presentations for Subgroups, \indexit{465}
  `NextIterator', 271
  `NextPrimeInt', 131
  `NF', 577
  `NiceBasis', 598
  `NiceBasisFiltersInfo', 599
  `NiceFreeLeftModule', 597
  `NiceFreeLeftModuleInfo', 598
  `NiceMonomorphism', 380
  `NiceMonomorphismAutomGroup', 383
  Nice Monomorphisms, \indexit{379}
  `NiceObject', 380
  `NiceVector', 597
  `NilpotencyClassOfGroup', 356
  `NilpotentQuotientOfFpLieAlgebra', 639
  `NK', 158
  `NOAUTO', 829
  `NonnegativeIntegers', 125
  `NonnegIntScalarProducts', 798, 799
  `NonNilpotentElement', 637
  `Norm', 569
    \sub of character, 760
  `NormalBase', 570
  `NormalClosure', 352
  `NormalFormIntMat', 236
  Normal Forms of Integer Matrices - Name Changes, \indexit{832}
  Normal Forms over the Integers, \indexit{234}
  `NormalIntersection', 352
  `Normalized\-Element\-Of\-Magma\-Ring\-Modulo\-Relations', 651
  `NormalizedWhitespace', 248
  `Normalizer', 351
  normalizer, 351
  `NormalizerInGLnZ', 424
  `NormalizerInGLnZBravaisGroup', 424
  `NormalizersTom', 698
  `NormalizerTom', 698
  `NormalizeWhitespace', 248
  `NormalSeriesByPcgs', 437
  Normal Structure, \indexit{351}
  `NormalSubgroupClasses', 748
  `NormalSubgroupClassesInfo', 747
  `NormalSubgroups', 364
  `NormedRowVector', 210
  `NormedRowVectors', 594
  `NormedVectors', 833
  `not', 167
  `NrArrangements', 145
  `NrBasisVectors', 591
  `NrCombinations', 145
  `NrConjugacyClasses', 350
    \sub for character tables, 720
  `NrConjugacyClassesGL', 505
  `NrConjugacyClassesGU', 505
  `NrConjugacyClassesPGL', 505
  `NrConjugacyClassesPGU', 505
  `NrConjugacyClassesPSL', 505
  `NrConjugacyClassesPSU', 505
  `NrConjugacyClassesSL', 505
  `NrConjugacyClassesSLIsogeneous', 505
  `NrConjugacyClassesSU', 505
  `NrConjugacyClassesSUIsogeneous', 505
  `NrDerangements', 148
  `NrInputsOfStraightLineProgram', 332
  `NrMovedPoints', 403
  `NrOrderedPartitions', 149
  `NrPartitions', 149
  `NrPartitionsSet', 148
  `NrPartitionTuples', 151
  `NrPermutationsList', 147
  `NrPolyhedralSubgroups', 730
  `NrPrimitiveGroups', 516
  `NrRestrictedPartitions', 150
  `NrSubsTom', 694
  `NrTransitiveGroups', 507
  `NrTuples', 147
  `NrUnorderedTuples', 146
  `NullAlgebra', 604
  `NullMat', 219
  `NullspaceIntMat', 233
  `NullspaceMat', 222
  `NullspaceMatDestructive', 222
  `NullspaceModQ', 231
  `Number', 197
  number, Bell, 144
    \sub binomial, 143
    \sub Stirling, of the first kind, 144
    \sub Stirling, of the second kind, 145
  `NumberArgumentsFunction', 60
  `NumberFFVector', 211
  number field, 578
  number fields, Galois group, 581
  `NumberIrreducibleSolvableGroups', 518
  `NumberPerfectGroups', 512
  `NumberPerfectLibraryGroups', 512
  `NumberSmallGroups', 509
  `NumberSyllables', 328
  numerator, of a rational, 142
  `NumeratorOfModuloPcgs', 433
  `NumeratorOfRationalFunction', 657
  `NumeratorRat', 142
  Numerical Group Attributes, \indexit{358}
\letter O
  $O_p(G)$, see `PCore', 351
  `ObjByExtRep', 644
  Objects, \indexit{109}
  obsolete, 832
  `OCOneCocycles', 372
  octal character codes, 244
  `OctaveAlgebra', 604
  `od', 51
  `OldGeneratorsOfPresentation', 487
  `Omega', 355
  `ONanScottType', 408
  `OnBreak', 67
  `OnBreakMessage', 68
  `One', 285
  `OneAttr', 285
  `OneCoboundaries', 371
  `OneCocycles', 370
  one cohomology, 370
  `OneFactorBound', 664
  `OneImmutable', 285
  `OneIrreducibleSolvableGroup', 518
  `One<Library>Group', 507
  `OneMutable', 285
  `OneOfPcgs', 428
  `OneOp', 285
  `OnePrimitiveGroup', 507
  `OneSameMutability', 285
  `OneSM', 285
  `OneSmallGroup', 509
  `OneTransitiveGroup', 507
  `OnIndeterminates', 662
    \sub as a permutation action, 389
  `OnLeftInverse', 388
  `OnLines', 389
    \sub example, 502
  `OnPairs', 388
  `OnPoints', 388
  `OnRight', 388
  `OnSets', 388
  `OnSetsDisjointSets', 388
  `OnSetsSets', 388
  `OnSetsTuples', 388
  `OnSubspacesByCanonicalBasis', 390
  `OnTuples', 388
  `OnTuplesSets', 388
  `OnTuplesTuples', 389
  `Operation', 832
  `OperationAlgebraHomomorphism', 616
  Operational Structure of Domains, \indexit{279}
  `OperationHomomorphism', 832
  operations, for booleans, 166
  Operations and Attributes for Vector Spaces, \indexit{585}
  Operations applicable to All Streams, \indexit{97}
  Operations Concerning Blocks, \indexit{725}
  Operations for (Near-)Additive Magmas, \indexit{548}
  Operations for Abelian Number Fields, \indexit{578}
  operations for algebraic elements, 677
  Operations for Associative Words, \indexit{326}
  Operations for Associative Words by their Syllables, \indexit{328}
  Operations for Booleans, \indexit{166}
  Operations for Brauer Characters, \indexit{781}
  Operations for Class Functions, \indexit{759}
  Operations for Collections, \indexit{267}
  Operations for Cyclotomics, \indexit{153}
  Operations for Domains, \indexit{284}
  Operations for Finite Field Elements, \indexit{573}
  Operations for Finitely Presented Groups, \indexit{456}
  Operations for Group Homomorphisms, \indexit{377}
  Operations for Input Streams, \indexit{97}
  Operations for Lists, \indexit{192}
  Operations for Output Streams, \indexit{100}
  Operations for Pc Groups, \indexit{448}
  Operations for Rational Functions, \indexit{656}
  Operations for Special Kinds of Bases, \indexit{590}
  Operations for Stabilizer Chains, \indexit{414}
  Operations for Vector Space Bases, \indexit{588}
  Operations for Words, \indexit{320}
  Operations on elements of the algebra, \indexit{337}
  Operations on rewriting systems, \indexit{336}
  Operations to Evaluate Strings, \indexit{250}
  Operations to Produce or Manipulate Strings, \indexit{247}
  Operations which have Special Methods for Groups with Pcgs, \indexit{441}
  operators, 41
    \sub arithmetic, 47
    \sub associativity, 48
    \sub for cyclotomics, 157
    \sub for lists, 178
    \sub precedence, 47, 48
  Operators for Character Tables, \indexit{717}
  Operators for Matrices, \indexit{216}
  Operators for Row Vectors, \indexit{208}
  Optimization and Compiler Options, \indexit{821}
  options, 27, 813
    \sub command line, filenames, 29
    \sub command line, internal, 30
  options, under UNIX, 27
  `or', 166
  `Orbit', 390
  `OrbitFusions', 792
  `OrbitLength', 391
  `OrbitLengths', 391
  `OrbitLengthsDomain', 391
  `OrbitPerms', 406
  `OrbitPowerMaps', 787
  `Orbits', operation/attribute, 390
  Orbits, \indexit{390}
  `OrbitsDomain', 390
  `OrbitsPerms', 406
  `OrbitStabChain', 415
  `OrbitStabilizer', 391
  `OrbitStabilizerAlgorithm', 392
  Orbit Stabilizer Methods for Polycyclic Groups, \indexit{440}
  `Order', 288
    \sub of a class function, 756
  order,  of a group, 341
    \sub of a list, collection or domain, 266
    \sub of the prime residue group, 134
  `OrderedPartitions', 149
  ordering, booleans, 165
    \sub of records, 257
  `OrderingByLessThanFunctionNC', 273
  `OrderingByLessThanOrEqualFunctionNC', 273
  `OrderingOfRewritingSystem', 336
  `OrderingOnGenerators', 275
  `OrderingsFamily', 273
  Orderings on families of associative words, \indexit{274}
  `OrderMod', 135
  `OrderOfRewritingSystem', 336
  `OrdersClassRepresentatives', 721
  `OrdersTom', 694
  `Ordinal', 251
  ordinary character, 759
  `OrdinaryCharacterTable', 719
  `OrthogonalComponents', 772
  Orthogonal Embeddings, \indexit{239}
  `OrthogonalEmbeddings', 239
  `OrthogonalEmbeddingsSpecialDimension', 768
  OSX, 822
  Other Filters, \indexit{124}
  Other Operations Applicable to any Object, \indexit{114}
  Other Operations for Character Tables, \indexit{728}
  Other Operations for Tables of Marks, \indexit{697}
  output, suppressing, 63
  `OutputLogTo', 94
    \sub for streams, 101
    \sub stop logging output, 94
  `OutputTextFile', 102
  `OutputTextNone', 105
  `OutputTextString', 103
  `OutputTextUser', 103
\letter P
  $p$-group, 358
  package, 828
  Package Interface - Obsolete Functions and Name Changes, \indexit{832}
  Packages, \indexit{817}
  `PadicCoefficients', 238
  `PadicExtensionNumberFamily', 680
  `PadicNumber', 680
    \sub for pure padics, 679
  `Pager', 25
  `Parametrized', 795
  Parametrized Maps, \indexit{793}
  parametrized maps, 784
  `Parent', 283
  `ParentPcgs', 431
  Parents, \indexit{283}
  partial order, 308
  `PartialOrderByOrderingFunction', 309
  `PartialOrderOfHasseDiagram', 308
  `Partitions', 149
  partitions, improper, of an integer, 149
    \sub ordered, of an integer, 149
    \sub restricted, of an integer, 150
  `PartitionsGreatestEQ', 150
  `PartitionsGreatestLE', 150
  `PartitionsSet', 148
  `PartitionTuples', 151
  `PcElementByExponents', 429
  `PcElementByExponentsNC', 429
  `PCentralLieAlgebra', 636
  `PCentralNormalSeriesByPcgsPGroup', 436
  `PCentralSeries', 361
  `PcGroupCode', 451
  `PcGroupCodeRec', 451
  `PcGroupFpGroup', 445
  Pc groups versus fp groups, \indexit{444}
  `PcGroupWithPcgs', 447
  `Pcgs', 427
  `Pcgs_OrbitStabilizer', 441
  Pcgs and Normal Series, \indexit{434}
  `PcgsByPcSequence', 427
  `PcgsByPcSequenceNC', 427
  `PcgsCentralSeries', 435
  `PcgsChiefSeries', 436
  `PcgsElementaryAbelianSeries', 435
  `PcgsPCentralSeriesPGroup', 436
  `PClassPGroup', 358
  `PCore', 351
  `PcSeries', 428
  `PerfectGroup', 511
  perfect groups, 511
  `PerfectIdentification', 512
  `PerfectResiduum', 353
  `Perform', 194
  `Permanent', 152
  Permanent of a Matrix, \indexit{152}
  `PermBounds', 781
  `PermCharInfo', 776
  `PermCharInfoRelative', 777
  `PermChars', 777
  `PermCharsTom', 707
  `PermComb', 781
  `PermLeftQuoTransformation', 545
  `PermList', 404
  `PermListList', 194
  `Permutation', 396
  `PermutationCharacter', 758
  permutation character, 803
  permutation characters, possible, 775, 777
  `PermutationCycle', 396
  `PermutationMat', 220
  `PermutationsFamily', 402
  Permutations Induced by Elements and Cycles, \indexit{396}
  `PermutationsList', 147
  `PermutationTom', 692
  `Permuted', 196
    \sub as a permutation action, 389
    \sub for class functions, 756
  `PGL', 503
  `PGU', 504
  `Phi', 134
  point stabilizer, 391
  Polycyclic Generating Systems, \indexit{426}
  `PolynomialByExtRep', 674
  `PolynomialCoefficientsOfPolynomial', 660
  `PolynomialDivisionAlgorithm', 670
  Polynomial Factorization, \indexit{662}
  `PolynomialModP', 663
  `PolynomialReducedRemainder', 670
  `PolynomialReduction', 670
  `PolynomialRing', 665
  Polynomial Rings, \indexit{665}
  Polynomials as Univariate Polynomials in one Indeterminate, \indexit{660}
  polynomials over abelian number fields, factors, 578
  Polynomials over the Rationals, \indexit{663}
  `PopOptions', 87
  Portability, \indexit{89}
  Porting GAP, \indexit{821}
  `Position', 185
  `PositionBound', 187
  `PositionCanonical', 185
  `PositionNonZero', 187
  `PositionNot', 187
  `PositionNthOccurrence', 186
  `PositionProperty', 187
  `PositionSet', 186
  `PositionSorted', 186
  `PositionStream', 99
  `PositionSublist', 188
  `PositionWord', 327
  `PositiveIntegers', 125
  positive number, 47
  `PositiveRoots', 632
  `PositiveRootVectors', 632
  `PossibleClassFusions', 791
  `PossibleFusionsCharTableTom', 706
  Possible Permutation Characters, \indexit{775}
  possible permutation characters, 775, 777
  `PossiblePowerMaps', 785
  power, 47
    \sub matrix, 217
    \sub meaning for class functions, 755
    \sub of words, 326
  `PowerMap', 785
  `PowerMapByComposition', 787
  `PowerMapOp', 785
  Power Maps, \indexit{784}
  `PowerMapsAllowedBySymmetrizations', 802
  `PowerMod', 560
  `PowerModCoeffs', 214
  `PowerModInt', 130
  `PowerPartition', 151
  powerset, 145
  `PowerSubalgebraSeries', 609
  `PQuotient', 467
  precedence, 47
  precedence test, for permutations, 403
  `PrefrattiniSubgroup', 353
    \sub for groups with pcgs, 441
  `PreImage', 301
  `PreImageElm', 300
  `PreImages', 301
  `PreImagesElm', 300
  Preimages in the Free Group, \indexit{455}
  Preimages in the Free Semigroup, \indexit{539}
  `PreimagesOfTransformation', 544
  `PreImagesRange', 300
  `PreImagesRepresentative', 301
  `PreImagesSet', 301
  Preimages under Homomorphisms from an FpGroup, \indexit{466}
  Preimages under Mappings, \indexit{300}
  preorder, 308
  `PresentationFpGroup', 471
  `PresentationNormalClosure', 476
  `PresentationNormalClosureRrs', 476
  `PresentationSubgroup', 473
  `PresentationSubgroupMtc', 475
  `PresentationSubgroupRrs', 474
  `PresentationViaCosetTable', 472
  previous result, 63
  `PrevPrimeInt', 131
  `PrimaryGeneratorWords', 475
  primary subgroup generators, 489
  `PrimeBlocks', 725
  `PrimeBlocksOp', 725
  `PrimeField', 568
  Prime Integers and Factorization, \indexit{130}
  `PrimePGroup', 358
  `PrimePowersInt', 132
  prime residue group, 134
    \sub exponent, 134
    \sub generator, 136
    \sub order, 134
  Prime Residues, \indexit{134}
  `PrimeResidues', function, 134
  `Primes', 130
  primitive, 397
  `PRIMITIVE_INDICES_MAGMA', 517
  `PrimitiveElement', 568
  `PrimitiveGroup', 516
  Primitive Groups, \indexit{408}
  `PrimitiveGroupsIterator', 516
  `PrimitiveIdentification', 517
  `PrimitiveIndexIrreducibleSolvableGroup', 518
  Primitive Permutation Groups, \indexit{515}
  `PrimitivePolynomial', 663
  `PrimitiveRoot', 575
  `PrimitiveRootMod', 136
  primitive root modulo an integer, 136
  Primitive Roots and Discrete Logarithms, \indexit{135}
  Primitivity of Characters, \indexit{807}
  `Print', 64
  `PrintAmbiguity', 798
  `PrintArray', 221
  `PrintCharacterTable', 733
  `PrintFactorsInt', 132
  `PrintFormattingStatus', 101
  Printing Character Tables, \indexit{731}
  Printing Class Functions, \indexit{756}
  Printing Presentations, \indexit{477}
  Printing Tables of Marks, \indexit{690}
  `PrintObj', 65
    \sub for character tables, 731, 756
    \sub for tables of marks, 691
  `PrintTo', 94
    \sub for streams, 100
  `ProbabilityShapes', 663
  problems, 818
  Problems on Particular Systems, \indexit{821}
  procedure call, 49
  Procedure Calls, \indexit{49}
  procedure call with arguments, 49
  `Process', 107
  Process, \indexit{107}
  `PROD_GF2MAT_GF2MAT_ADVANCED', 231
  `PROD_GF2MAT_GF2MAT_SIMPLE', 231
  `Product', 198
  product, of words, 326
    \sub rational functions, 656
  `ProductCoeffs', 213
  `ProductSpace', 609
  `ProductX', 201
  `ProfileFunctions', 81
  `ProfileGlobalFunctions', 81
  `ProfileMethods', 81
  `ProfileOperations', 80
  `ProfileOperationsAndMethods', 80
  `PROFILETHRESHOLD', 81
  Profiling, \indexit{80}
  `ProjectedInducedPcgs', 434
  `ProjectedPcElement', 434
  `Projection', 298
    \sub example for direct products, 494
    \sub example for semidirect products, 496
    \sub example for subdirect products, 496
    \sub example for wreath products, 497
    \sub for group products, 498
  `ProjectionMap', 794
  projections, find all, 384
  `ProjectiveActionHomomorphismMatrixGroup', 421
  `ProjectiveActionOnFullSpace', 421
  `ProjectiveGeneralLinearGroup', 503
  `ProjectiveGeneralUnitaryGroup', 504
  `ProjectiveOrder', 230
  `ProjectiveSpecialLinearGroup', 504
  `ProjectiveSpecialUnitaryGroup', 504
  `ProjectiveSymplecticGroup', 504
  prompt, 63
    \sub partial, 63
  Properties, \indexit{123}
  Properties and Attributes for Lists, \indexit{188}
  Properties and Attributes of (General) Mappings, \indexit{298}
  Properties and Attributes of Binary Relations, \indexit{307}
  Properties and Attributes of Matrices, \indexit{218}
  Properties and Attributes of Rational Functions, \indexit{657}
  Properties and basic functionality, \indexit{273}
  Properties of a Lie Algebra, \indexit{630}
  Properties of rewriting systems, \indexit{337}
  Properties of Rings, \indexit{555}
  Properties of Tables of Marks, \indexit{696}
  `PRump', 354
  `PseudoRandom', 269
  `PSL', 504
  `PSP', 504
  `PSp', 504
  `PSU', 504
  `PthPowerImage', 636
  `PthPowerImages', 635
  Pure p-adic Numbers, \indexit{679}
  `PurePadicNumberFamily', 679
  `PushOptions', 87
\letter Q
  `Quadratic', 160
  quadratic residue, 136, 137
  `QuaternionAlgebra', 604
  `QUIET', 833
  `QUIT', emergency quit, 71
  quit, in emergency, 71
  `quit', 66
  `QUITTING', 71
  `QuoInt', 128
  `Quotient', 551
  quotient, for finitely presented groups, 454
    \sub matrices, 217
    \sub matrix and matrix list, 218
    \sub matrix and scalar, 217
    \sub of free monoid, 540
    \sub of free semigroup, 538
    \sub of words, 326
    \sub rational functions, 656
    \sub scalar and matrix, 217
    \sub scalar and matrix list, 217
    \sub vector and matrix, 217
  `QuotientFromSCTable', 603
  Quotient Methods, \indexit{467}
  `QuotientMod', 560
  `QuotientPolynomialsExtRep', 675
  `QuotientRemainder', 559
  Quotients, \indexit{530}
  Quotients and Remainders, \indexit{128}
  `QuotientSemigroupCongruence', 530
  `QuotientSemigroupHomomorphism', 530
  `QuotientSemigroupPreimage', 530
  `QuotRemLaurpols', 665
\letter R
  $r_N$, 158
  `RadicalGroup', 353
  `RadicalOfAlgebra', 612
  `Random', 269
    \sub for integers, 127
    \sub for rationals, 142
  `RandomBinaryRelationOnPoints', 309
  random element, of a list or collection, 269
  Random Elements, \indexit{269}
  `RandomInvertibleMat', 221
  `RandomIsomorphismTest', 452
  Random Isomorphism Testing, \indexit{452}
  Randomized Methods for Permutation Groups, \indexit{410}
  `RandomList', 270
  `RandomMat', 221
  Random Matrices, \indexit{221}
  random seed, 270
  `RandomTransformation', 543
  `RandomUnimodularMat', 221
  `Range', 299
  range, 201
  Ranges, \indexit{201}
  `RankAction', 397
  `RankFilter', 116
  `RankMat', 222
  `RankOfTransformation', 544
  `RankPGroup', 358
  `Rat', 142
    \sub for strings, 250
  `RationalClass', 350
  `RationalClasses', 351
  `RationalFunctionByExtRep', 674
  `Rational\-Function\-By\-Ext\-Rep\-With\-Cancellation', 675
  Rational Function Families, \indexit{672}
  `RationalFunctionsFamily', 672
  `RationalizedMat', 161
  `Rationals', 141
  `RClassOfHClass', 531
  `Read', 93
    \sub for streams, 97
  `ReadAll', 99
  `ReadAllLine', 104
  `ReadAsFunction', 93
    \sub for streams, 98
  `ReadByte', 98
  read eval print loop, 63
  `ReadLine', 98
  `ReadPackage', 829
  `ReadPkg', 832
  `ReadTest', 83
    \sub for streams, 98
  `RealClasses', 723
  `RealizableBrauerCharacters', 782
  `RecNames', 254
  Recognizing Characters, \indexit{246}
  record, component access, 254
    \sub component assignment, 255
    \sub component variable, 255
    \sub component variable assignment, 256
  Record Access Operations, \indexit{259}
  Record Assignment, \indexit{255}
  record assignment, operation, 259
  record boundness test, operation, 259
  record component, operation, 259
  record unbind, operation, 259
  Recovery from NoMethodFound-Errors, \indexit{75}
  recursion, 54
  redisplay a help section, 23
  redisplay with next help viewer, 23
  `ReduceCoeffs', 214
  `ReduceCoeffsMod', 214
  `ReducedAdditiveInverse', 337
  `ReducedCharacters', 765
  `ReducedClassFunctions', 765
  `ReducedComm', 337
  `ReducedConfluentRewritingSystem', 540
  `ReducedConjugate', 337
  `ReducedDifference', 337
  `ReducedForm', 336
  `ReducedGroebnerBasis', 671
  `ReducedInverse', 337
  `ReducedLeftQuotient', 337
  `ReducedOne', 337
  `ReducedPcElement', 429
  `ReducedPower', 337
  `ReducedProduct', 337
  `ReducedQuotient', 337
  `ReducedScalarProduct', 337
  `ReducedSum', 337
  `ReducedZero', 337
  `ReduceRules', 337
  `ReduceStabChain', 416
  Reducing Virtual Characters, \indexit{765}
  `Ree', 501
  `ReeGroup', 501
  `ReesCongruenceOfSemigroupIdeal', 529
  `ReesMatrixSemigroup', 532
  `ReesMatrixSemigroupElement', 532
  Rees Matrix Semigroups, \indexit{532}
  `ReesZeroMatrixSemigroup', 532
  `ReesZeroMatrixSemigroupElement', 532
  `ReesZeroMatrixSemigroupElementIsZero', 533
  `RefinedPcGroup', 447
  `ReflectionMat', 221
  `ReflexiveClosureBinaryRelation', 309
  reflexive relation, 307
  regular, 397
  regular action, 394
  `RegularActionHomomorphism', 395
  `RegularModule', 736
  relations, 296
  Relations Between Domains, \indexit{289}
  `RelationsOfFpSemigroup', 539
  `RelativeBasis', 588
  `RelativeBasisNC', 588
  relatively prime, 47
  `RelativeOrderOfPcElement', 428
  `RelativeOrders', of a pcgs, 428
  Relators in a Presentation, \indexit{476}
  `RelatorsOfFpGroup', 455
  remainder, operation, 289
  remainder of a quotient, 128
  `RemInt', 128
  remove, an element from a set, 192
  `RemoveFile', 94
  `RemoveOuterCoeffs', 212
  `RemoveRelator', 479
  `RemoveSet', 192
  `RemoveStabChain', 416
  Repeat, \indexit{51}
  `repeat' loop, 51
  `ReplacedString', 248
  Representation, \indexit{119}
  representation, as a sum of two squares, 139
  Representations for Associative Words, \indexit{329}
  Representations for Group Homomorphisms, \indexit{385}
  Representations given by modules, \indexit{736}
  Representations of Algebras, \indexit{617}
  `RepresentationsOfObject', 120
  `Representative', 266
  representative, of a list or collection, 266
  `RepresentativeAction', 392
  `RepresentativeLinearOperation', 617
  `RepresentativeOperation', 832
  `RepresentativesContainedRightCosets', 348
  `RepresentativesFusions', 792
  `RepresentativeSmallest', 266
  `RepresentativesMinimalBlocks', 398
  `RepresentativesPerfectSubgroups', 366
  `RepresentativesPowerMaps', 787
  `RepresentativesSimpleSubgroups', 366
  `RepresentativeTom', 705
  `RepresentativeTomByGenerators', 705
  `RepresentativeTomByGeneratorsNC', 705
  `RequirePackage', 832
  `Reread', 95
  `REREADING', 95
  `RereadPackage', 829
  `RereadPkg', 832
  `ResetOptionsStack', 87
  residue, quadratic, 136, 137
  Residue Class Rings, \indexit{132}
  `RespectsAddition', 303
  `RespectsAdditiveInverses', 303
  `RespectsInverses', 303
  `RespectsMultiplication', 302
  `RespectsOne', 303
  `RespectsScalarMultiplication', 304
  `RespectsZero', 304
  `RestoreStateRandom', 269
  Restricted and Induced Class Functions, \indexit{763}
  `RestrictedClassFunction', 763
  `RestrictedClassFunctions', 764
  Restricted Lie algebras, \indexit{635}
  `RestrictedMapping', 298
  `RestrictedPartitions', 150
  `RestrictedPerm', 405
  `RestrictedTransformation', 544
  `Resultant', 661
  `ResultOfStraightLineProgram', 332
  Return, \indexit{57}
  `return', 66
    \sub no value, 57
    \sub with value, 57
  `ReturnFail', 61
  `ReturnFalse', 61
  return from break loop, 66
  `ReturnTrue', 61
  `Reversed', 194
  `RewindStream', 99
  `RewriteWord', 461
  Rewriting in Groups and Monoids, \indexit{338}
  Rewriting Systems and the Knuth-Bendix Procedure, \indexit{540}
  `RightActingAlgebra', 620
  `RightActingRingOfIdeal', 554
  `RightAlgebraModule', 618
  `RightAlgebraModuleByGenerators', 618
  `RightCoset', 346
  `RightCosets', 347
  right cosets, 346
  `RightCosetsNC', 347
  `RightDerivations', 627
  `RightIdeal', 552
  `RightIdealByGenerators', 553
  `RightIdealNC', 553
  `RightModuleByHomomorphismToMatAlg', 621
  `RightShiftRowVector', 212
  `RightTransversal', 347
  `Ring', 550
  `RingByGenerators', 551
  Ring Homomorphisms, \indexit{305}
  Rings With One, \indexit{554}
  `RingWithOne', 554
  `RingWithOneByGenerators', 554
  `RNamObj', 259
  root, of 1 modulo an integer, 138
    \sub of an integer, 127
    \sub of an integer, smallest, 127
    \sub of an integer modulo another, 137
  `RootInt', 127
  `RootMod', 137
  `RootOfDefiningPolynomial', 568
  `RootsMod', 137
  Roots Modulo Integers, \indexit{136}
  roots of unity, 153
  `RootsOfUPol', 660
  `RootsUnityMod', 138
  `RootSystem', 632
  `RoundCyc', 155
  Row and Matrix Spaces, \indexit{592}
  `RowIndexOfReesMatrixSemigroupElement', 533
  `Row\-Index\-Of\-Rees\-Zero\-Matrix\-Semigroup\-Element', 533
  row spaces, 592
  Row Vectors over Finite Fields, \indexit{210}
  `Rules', 336
  Running GAP under MacOS, \indexit{30}
  `Runtime', 80
  `Runtimes', 79
\letter S
  $s_N$, 158
  `SameBlock', 726
  `SandwichMatrixOfReesMatrixSemigroup', 533
  `SandwichMatrixOfReesZeroMatrixSemigroup', 533
  save, 36
  `SaveOnExitFile', 72
  `SaveWorkspace', 36
  Saving and Loading a Workspace, \indexit{36}
  Saving a Pc Group, \indexit{448}
  saving on exit, 71
  `ScalarProduct', for characters, 760
  Schreier, 473
  Schreier-Sims, random, 410
  `SchurCover', 372
  Schur Covers and Multipliers, \indexit{372}
  Schur multiplier, 373
  scope, 41
  `ScriptFromString', 701
  Searching for Homomorphisms, \indexit{383}
  `SecHMSM', 252
  secondary subgroup generators, 489
  `SecondsDMYhms', 252
  `SeekPositionStream', 100
  Selecting a Different MeatAxe, \indexit{682}
  Selection Functions, \indexit{506}
  `SemidirectProduct', 495
  Semidirect Products, \indexit{494}
  `SemiEchelonBasis', 594
  `SemiEchelonBasisNC', 594
  `SemiEchelonMat', 224
  `SemiEchelonMatDestructive', 224
  `SemiEchelonMats', 225
  `SemiEchelonMatsDestructive', 225
  `SemiEchelonMatTransformation', 225
  `Semigroup', 527
  semigroup, 527
  `SemigroupByGenerators', 527
  `SemigroupByMultiplicationTable', 528
  `SemigroupIdealByGenerators', 529
  `SemigroupOfRewritingSystem', 542
  semiregular, 397
  Semisimple Lie Algebras and Root Systems, \indexit{631}
  `SemiSimpleType', 631
  sequence, Bernoulli, 144
    \sub Fibonacci, 151
    \sub Lucas, 152
  Series of Ideals, \indexit{629}
  `Set', 263
  `SetAssertionLevel', 79
  `SetCommutator', 446
  `SetConjugate', 446
  `SetCrystGroupDefaultAction', 425
  set difference, of collections, 268
  `SetEntrySCTable', 602
  `SetGasmanMessageStatus', 85
  `SetHelpViewer', 24
  `SetIndeterminateName', 655
  `SetInfoLevel', 78
  `SetName', 114
  Set Operations via Boolean Lists, \indexit{205}
  `SetParent', 283
  `SetPower', 446
  `SetPrintFormattingStatus', 101
  `SetRecursionTrapInterval', 84
  `SetReducedMultiplication', 455
  Sets, \indexit{109}
  sets, 168, 190
  Sets of Subgroups, \indexit{363}
  set stabilizer, 391
  `Setter', 121
  setter, 120
  Setter and Tester for Attributes, \indexit{120}
  `SetX', 200
  `ShallowCopy', 113
    \sub for lists, 175
  `ShiftedCoeffs', 214
  `ShiftedPadicNumber', 679
  Shifting and Trimming Coefficient Lists, \indexit{212}
  `ShortestVectors', 240
  `ShortLexOrdering', 276
  short vectors spanning a lattice, 238, 766
  `ShowArgument', 75
  `ShowArguments', 75
  `ShowDetails', 75
  `ShowImpliedFilters', 117
  `ShowMethods', 75
  `ShowOtherMethods', 76
  `ShrinkCoeffs', 214
  `ShrinkRowVector', 212
  `SiftedPcElement', 429
  `SiftedPermutation', 415
  `SiftedVector', 595
  `Sigma', 138
  sign, of an integer, 126
  Sign and Cycle Structure, \indexit{404}
  `SignInt', 126
  `SignPartition', 150
  `SignPerm', 404
  `SimpleLieAlgebra', 627
  `SimpleSystem', 632
  `SimplifiedFpGroup', 473
  SimplifiedFpGroup, \indexit{473}
  `SimplifyPresentation', 480
  `SimsNo', 517
  `SimultaneousEigenvalues', 230
  `SingleCollector', 446
  singlequote character, 244
  singlequotes, 242
  `SINT_CHAR', 250
  `Size', 266
    \sub for character tables, 720
    \sub for groups with pcgs, 441
  size, of a list or collection, 266
  `SizeBlist', 205
  `SizeConsiderFunction', 369
  `SizeNumbersPerfectGroups', 512
  `SizeOfFieldOfDefinition', 782
  `SizesCentralizers', 721
  `SizesConjugacyClasses', 721
  `SizeScreen', 74
  SizeScreen, \indexit{74}
  `SizesPerfectGroups', 511
  `SizeStabChain', 414
  `SL', 502
  smaller, associative words, 326
    \sub elements of finitely presented groups, 455
    \sub nonassociative words, 319
    \sub pcwords, 444
    \sub rational functions, 656
  `SmallerDegreePermutationRepresentation', 407
  smaller or equal, 46
  smaller test, 46
  `SmallestGeneratorPerm', 403
  `SmallestMovedPoint', 403
  `SmallestRootInt', 127
  `SmallGeneratingSet', 370
  `SmallGroup', 509
  Small Groups, \indexit{508}
  `SmallGroupsInformation', 509
  Smash MeatAxe Flags, \indexit{686}
  smith normal form, 832
  `SmithNormalFormIntegerMat', 235
  `SmithNormalFormIntegerMatTransforms', 235
  `SMTX.AbsoluteIrreducibilityTest', 686
  `SMTX.AlgEl', 686
  `SMTX.AlgElCharPol', 687
  `SMTX.AlgElCharPolFac', 687
  `SMTX.AlgElMat', 686
  `SMTX.AlgElNullspaceDimension', 687
  `SMTX.AlgElNullspaceVec', 687
  `SMTX.CentMat', 687
  `SMTX.CentMatMinPoly', 687
  `SMTX.CompleteBasis', 686
  `SMTX.Getter', 686
  `SMTX.GoodElementGModule', 686
  `SMTX.IrreducibilityTest', 686
  `SMTX.MatrixSum', 686
  `SMTX.MinimalSubGModule', 686
  `SMTX.MinimalSubGModules', 686
  `SMTX.RandomIrreducibleSubGModule', 686
  `SMTX.Setter', 686
  `SMTX.SortHomGModule', 686
  `SMTX.Subbasis', 686
  `SO', 503
  `Socle', 354
  `SocleTypePrimitiveGroup', 408
  `SolutionIntMat', 233
  `SolutionMat', 223
  `SolutionMatDestructive', 223
  `SolutionNullspaceIntMat', 233
  Some Remarks about Character Theory in GAP, \indexit{709}
  Some Special Algebras, \indexit{604}
  `Sort', 189
  `SortedCharacters', 743
  `SortedCharacterTable', 744
  Sorted Character Tables, \indexit{743}
  `SortedList', 263
  sorted list, 188
  Sorted Lists and Sets, \indexit{190}
  sorted lists as collections, 261
  `SortedSparseActionHomomorphism', 394
  `SortedTom', 692
  `Sortex', 190
  Sorting Lists, \indexit{189}
  `SortingPerm', 190
  Sorting Tables of Marks, \indexit{692}
  `SortParallel', 189
  `Source', 299
  `SP', 503
  `Sp', 503
  space, 39
  `SparseActionHomomorphism', 394
  `SparseCartanMatrix', 633
  Special Characters, \indexit{244}
  special character sequences, 244
  Special Filenames, \indexit{91}
  Special Generating Sets, \indexit{369}
  `SpecialLinearGroup', 502
  Special Multiplication Algorithms for Matrices over GF(2), \indexit{231}
  `SpecialOrthogonalGroup', 503
  Special Pcgs, \indexit{437}
  `SpecialPcgs', attribute, 438
  `SpecialUnitaryGroup', 502
  Specific and Parametrized Subgroups, \indexit{352}
  Specific Methods for Subgroup Lattice Computations, \indexit{367}
  `SplitCharacters', 738
  `SplitExtension', 449
  `SplitExtensions', 450
  `SplitString', 247
  `SplittingField', 659
  `Sqrt', 289
  square root, of an integer, 127
  `SquareRoots', 316
  `SSortedList', 263
  `StabChain', 411
  `StabChainBaseStrongGenerators', 413
  `StabChainImmutable', 411
  `StabChainMutable', 411
  `StabChainOp', 411
  `StabChainOptions', 413
  `Stabilizer', 391
  Stabilizer Chain Records, \indexit{413}
  Stabilizer Chains, \indexit{409}
  `StabilizerOfExternalSet', 400
  `StabilizerPcgs', 441
  Stabilizers, \indexit{391}
  `StandardAssociate', 557
  `StandardGeneratorsFunctions', 702
  `StandardGeneratorsInfo', for groups, 700
    \sub for tables of marks, 705
  `StandardGeneratorsOfGroup', 702
  Standard Generators of Groups, \indexit{700}
  Standardization of coset tables, \indexit{460}
  `StandardizeTable', 460
  `StarCyc', 160
  Statements, \indexit{48}
  `StateRandom', 269
  `Stirling1', 144
  `Stirling2', 144
  Stirling number of the first kind, 144
  Stirling number of the second kind, 145
  `StoredGroebnerBasis', 671
  `StoreFusion', 790
  Storing Normal Subgroup Information, \indexit{747}
  `StraightLineProgElm', 335
  `StraightLineProgGens', 335
  `StraightLineProgram', 331
  Straight Line Program Elements, \indexit{334}
  `StraightLineProgramNC', 331
  Straight Line Programs, \indexit{331}
  `StraightLineProgramsTom', 704
  `StreamsFamily', 97
  `StretchImportantSLPElement', 335
  strictly sorted list, 189
  `String', 247
    \sub for cyclotomics, 154
  `StringDate', 252
  `StringOfResultOfStraightLineProgram', 333
  `StringPP', 247
  strings, equality of, 246
    \sub inequality of, 246
    \sub lexicographic ordering of, 246
  String Streams, \indexit{103}
  `StringTime', 252
  `StrongGeneratorsStabChain', 414
  `StronglyConnectedComponents', 309
  <Struct>, 280
  `<Struct>ByGenerators', 281
  `StructuralCopy', 113
    \sub for lists, 176
  structure constant, 730, 731
  `StructureConstantsTable', 590
  `<Struct>WithGenerators', 281
  `SU', 502
  `Subalgebra', 605
  `SubAlgebraModule', 621
  `SubalgebraNC', 605
  Subalgebras, \indexit{605}
  `SubalgebraWithOne', 605
  `SubalgebraWithOneNC', 606
  `SubdirectProduct', 496
  Subdirect Products, \indexit{496}
  `SubdirectProducts', 497
  subdomains, 284
  `Subfield', 567
  `SubfieldNC', 567
  `Subfields', 568
  Subfields of Fields, \indexit{567}
  `Subgroup', 343
  `SubgroupByPcgs', 432
  `SubgroupByProperty', 344
  subgroup fusions, 788
  subgroup generators tree, 489
  Subgroup Lattice, \indexit{365}
  `SubgroupNC', 343
  `SubgroupOfWholeGroupByCosetTable', 461
  `SubgroupOfWholeGroupByQuotientSubgroup', 466
  Subgroup Presentations, \indexit{473}
  `SubgroupProperty', 417
  Subgroups, \indexit{342}
  subgroups, polyhedral, 730
  Subgroups characterized by prime powers, \indexit{355}
  Subgroup Series, \indexit{359}
  `SubgroupShell', 344
  Subgroups of Polycyclic Groups - Canonical Pcgs, \indexit{432}
  Subgroups of Polycyclic Groups - Induced Pcgs, \indexit{430}
  `SubgroupsSolvableGroup', 368
  sublist, 170
    \sub access, 170
    \sub assignment, 172
    \sub operation, 171
  sublist assignment, operation, 173
  `Submagma', 313
  `SubmagmaNC', 313
  `SubmagmaWithInverses', 313
  `SubmagmaWithInversesNC', 313
  `SubmagmaWithOne', 313
  `SubmagmaWithOneNC', 313
  `Submodule', 563
  `SubmoduleNC', 563
  Submodules, \indexit{563}
  `Submonoid', 534
  `SubmonoidNC', 534
  `SubnearAdditiveGroup', 548
  `SubnearAdditiveGroupNC', 548
  `SubnearAdditiveMagma', 547
  `SubnearAdditiveMagmaNC', 547
  `SubnearAdditiveMagmaWithZero', 547
  `SubnearAdditiveMagmaWithZeroNC', 547
  `SubnormalSeries', 360
  `Subring', 551
  `SubringNC', 551
  `SubringWithOne', 555
  `SubringWithOneNC', 555
  Subroutines for the Construction of Class Fusions, \indexit{803}
  Subroutines for the Construction of Power Maps, \indexit{801}
  `Subsemigroup', 527
  `SubsemigroupNC', 527
  subsets, 145
  subset test, for collections, 267
  `Subspace', 584
  `SubspaceNC', 584
  `Subspaces', 585
  `SubstitutedWord', 328
  `SubsTom', 693
  `Sub<struct>', 284
  `Sub<struct>NC', 284
  `SubSyllables', 329
  subtract, a set from another, 192
  `SubtractBlist', 206
  subtraction, 47
    \sub matrices, 216
    \sub matrix and scalar, 216
    \sub rational functions, 656
    \sub scalar and matrix, 216
    \sub scalar and matrix list, 217
    \sub scalar and vector, 209
    \sub vector and scalar, 209
    \sub vectors, 209
  `SubtractSet', 192
  `Subword', 327
  `Successors', 308
  Suitability for Compilation, \indexit{35}
  `Sum', 199
  Sum and Intersection of Pcgs, \indexit{437}
  `SumFactorizationFunctionPcgs', 437
  `SumIntersectionMat', 226
  `SumX', 200
  `SupersolvableResiduum', 354
  `support', email address, 820
  `SupportedCharacterTableInfo', 713
  `SurjectiveActionHomomorphismAttr', 401
  `SuzukiGroup', 501
  `SylowComplement', 354
  `SylowSubgroup', 354
  Sylow Subgroups and Hall Subgroups, \indexit{354}
  `SylowSystem', 355
  Symbols, \indexit{39}
  Symmetric and Alternating Groups, \indexit{407}
  `SymmetricClosureBinaryRelation', 309
  `SymmetricGroup', 501
  symmetric group, powermap, 151
  `SymmetricParentGroup', 408
  `SymmetricParts', 772
  `SymmetricPowerOfAlgebraModule', 646
  symmetric relation, 307
  `Symmetrizations', 771
  symmetrizations, orthogonal, 772
    \sub symplectic, 773
  Symmetrizations of Class Functions, \indexit{771}
  `SymplecticComponents', 773
  `SymplecticGroup', 503
  syntax errors, 63
  system getter, 120
  system setter, 120
  `Sz', 501
\letter T
  $t_N$, 158
  `TableAutomorphisms', 746
  table automorphisms, 792, 804
  table of chapters for help books, 23
  `TableOfMarks', 689
  `TableOfMarksByLattice', 690
  `TableOfMarksComponents', 693
  `TableOfMarksCyclic', 707
  `TableOfMarksDihedral', 707
  `TableOfMarksFamily', 693
  `TableOfMarksFrobenius', 707
  Table of Marks Objects in GAP, \indexit{688}
  table of sections for help books, 23
  tables, 709, 711
  tabulator, 39
  `Tau', 138
  Technical Details about Tables of Marks, \indexit{693}
  Technical Details about the Implementation of Magma Rings, \indexit{652}
  Technical Matters Concerning General Mappings, \indexit{305}
  `TemporaryGlobalVarName', 44
  `Tensored', 763
  `TensorProductGModule ', 682
  `TensorProductOfAlgebraModules', 645
  Tensor Products and Exterior and Symmetric Powers, \indexit{645}
  test, for a primitive root, 136
    \sub for a rational, 141
    \sub for records, 254
    \sub for set equality, 191
  `TestConsistencyMaps', 797
  `Tester', 121
  tester, 120
  Test Files, \indexit{83}
  `TestHomogeneous', 807
  `TestInducedFromNormalSubgroup', 809
  Testing Finiteness of Finitely Presented Groups, \indexit{470}
  Testing for the System Architecture, \indexit{34}
  Testing Monomiality, \indexit{809}
  `TestJacobi', 602
  `TestMonomial', 809
  `TestMonomialQuick', 810
  `TestMonomialUseLattice', 810
  Test of the installation, \indexit{816}
  `TestPackageAvailability', 829
  `TestPerm1', 779
  `TestPerm2', 779
  `TestPerm3', 779
  `TestPerm4', 779
  `TestPerm5', 779
  `TestQuasiPrimitive', 808
  `TestRelativelySM', 811
  Tests for Actions, \indexit{396}
  Tests for the Availability of Methods, \indexit{373}
  `TestSubnormallyMonomial', 811
  The .gaprc file, \indexit{33}
  The Adjoint Representation, \indexit{636}
  The Compiler, \indexit{34}
  The Defining Attributes of Rational Functions, \indexit{673}
  The Dixon-Schneider Algorithm, \indexit{736}
  The Documentation, \indexit{818}
  The External Representation for Associative Words, \indexit{330}
  The family pcgs, \indexit{443}
  The Interface between Character Tables and Groups, \indexit{715}
  The Interface between Tables of Marks and Character Tables, \indexit{706}
  The Library of Tables of Marks, \indexit{708}
  `then', 50
  The Natural Action, \indexit{406}
  The Pager Command, \indexit{25}
  The Permutation Image of an Action, \indexit{393}
  The Representations of Rational Functions, \indexit{672}
  The Smash MeatAxe, \indexit{685}
  The Syntax in BNF, \indexit{57}
  `ThreeGroup' library, 508
  Tietze Options, \indexit{492}
  Tietze Transformations, \indexit{479}
  Tietze Transformations that introduce new Generators, \indexit{483}
  `TietzeWordAbstractWord', 477
  `time', 80
  Timing, \indexit{79}
  Todd-Coxeter Procedure, \indexit{542}
  `Trace', 218
    \sub for field elements, 569
    \sub of a matrix, 218
  `TracedCosetFpGroup', 457
  `TraceImmediateMethods', 77
  `TraceMat', 218
  `TraceMethods', 77
  `TracePolynomial', 569
  Tracing generator images through Tietze transformations, \indexit{487}
  Tracing Methods, \indexit{77}
  `TransferDiagram', 797
  `Transformation', 543
  `TransformationData', 543
  `TransformationFamily', 543
  `TransformationNC', 543
  `TransformationRelation', 545
  `TransformationType', 543
  `TransformingPermutations', 746
  `TransformingPermutationsCharacterTables', 746
  transitive, 396
  `TransitiveClosureBinaryRelation', 309
  `TransitiveGroup', 507
  `TransitiveIdentification', 507
  Transitive Permutation Groups, \indexit{507}
  transitive relation, 307
  `Transitivity', for characters, 762
    \sub for class functions, 762
    \sub for group actions, 397
  `TranslatorSubalgebra', 623
  transporter, 392
  `TransposedMat', 220
  `TransposedMatAttr', 220
  `TransposedMatDestructive', 220
  `TransposedMatImmutable', 220
  `TransposedMatMutable', 220
  `TransposedMatOp', 220
  `TransposedMatrixGroup', 420
  Transversals, \indexit{347}
  Triangular Matrices, \indexit{226}
  `TriangulizedIntegerMat', 234
  `TriangulizedIntegerMatTransform', 234
  `TriangulizedNullspaceMat', 222
  `TriangulizedNullspaceMatDestructive', 222
  `TriangulizeIntegerMat', 234
  `TriangulizeMat', 222
  `TrivialCharacter', 758
  `TrivialGroup', 499
  `TrivialIterator', 272
  `TrivialSubalgebra', 606
  `TrivialSubgroup', 352
  `TrivialSubmagmaWithOne', 316
  `TrivialSubmodule', 563
  `TrivialSubmonoid', 534
  `TrivialSubnearAdditiveMagmaWithZero', 548
  `TrivialSubspace', 585
  `Try\-Conway\-Polynomial\-For\-Frobenius\-Character\-Value', 782
  `TryCosetTableInWholeGroup', 461
  `TryGcdCancelExtRepPolynomials', 675
  `Tuples', 147
  tuple stabilizer, 391
  `TwoClosure', 417
  `TwoCoboundaries', 448
  `TwoCocycles', 448
  `TwoCohomology', 449
  `TwoGroup' library, 508
  `TwoSidedIdeal', 552
  `TwoSidedIdealByGenerators', 553
  `TwoSidedIdealNC', 553
  `TwoSquares', 139
  type, boolean, 165
    \sub cyclotomic, 153
    \sub records, 254
    \sub strings, 242
  `TypeObj', 124
  `TypeOfDefaultGeneralMapping', 306
  Types, \indexit{124}
  `TzEliminate', 482
  `TzFindCyclicJoins', 483
  `TzGo', 479
  `TzGoGo', 481
  `TzImagesOldGens', 487
  `TzInitGeneratorImages', 487
  `TzNewGenerator', 479
  `TzOptions', 492
  `TzPreImagesNewGens', 488
  `TzPrint', 478
  `TzPrintGeneratorImages', 488
  `TzPrintGenerators', 477
  `TzPrintLengths', 478
  `TzPrintOptions', 493
  `TzPrintPairs', 478
  `TzPrintPresentation', 478
  `TzPrintRelators', 477
  `TzPrintStatus', 478
  `TzSearch', 482
  `TzSearchEqual', 483
  `TzSort', 471
  `TzSubstitute', 484
  `TzSubstituteCyclicJoins', 487
\letter U
  $u_N$, 158
  `UglyVector', 597
  `Unbind', 42
    \sub for lists, 174
  `UnbindGlobal', 44
  `UnderlyingCharacteristic', 722
  `UnderlyingCharacterTable', 752
  `UnderlyingElement', fp group elements, 456
    \sub fp semigroup elements, 539
  `Underlying\-Element\-Of\-Rees\-Matrix\-Semigroup\-Element', 533
  `Underlying\-Element\-Of\-Rees\-Zero\-Matrix\-Semigroup\-Element', 533
  `UnderlyingExternalSet', 401
  `UnderlyingFamily', 626
  `UnderlyingGeneralMapping', 299
  `UnderlyingGroup', for character tables, 715
    \sub for tables of marks, 695
  `UnderlyingLeftModule', 588
  `UnderlyingLieAlgebra', 632
  `UnderlyingMagma', 649
  `UnderlyingRelation', 299
  `UnInstallCharReadHookFunc', 105
  `Union', 268
  union, of collections, 268
    \sub of sets, 192
  `Union2', 268
  `UnionBlist', 205
  `Unique', 193
  `UniteBlist', 206
  `UniteBlistList', 206
  `UniteSet', 192
  `Units', 556
  Units and Factorizations, \indexit{556}
  `UnivariatenessTestRationalFunction', 660
  `UnivariatePolynomial', 659
  `UnivariatePolynomialByCoefficients', 659
  `UnivariatePolynomialRing', 667
  Univariate Polynomial Rings, \indexit{667}
  Univariate Polynomials, \indexit{659}
  `Univariate\-Rational\-Function\-By\-Coefficients', 665
  Univariate Rational Functions, \indexit{665}
  `UniversalEnvelopingAlgebra', 638
  Universal Enveloping Algebras, \indexit{638}
  UNIX, features, 27
    \sub options, 27
  `UNIXSelect', 97
  `Unknown', 163
  `UnloadSmallGroupsData', 509
  `UnorderedTuples', 146
  Unpacking, \indexit{814}
  `UnprofileFunctions', 81
  `UnprofileMethods', 81
  `until', 51
  `UntraceMethods', 77
  `UpdateMap', 795
  `UpEnv', 69
  `UpperCentralSeriesOfGroup', 361
  `UpperSubdiagonal', 227
  `UseBasis', 564
  `UseFactorRelation', 290
  Useful Categories for all Elements of a Family, \indexit{293}
  Useful Categories of Elements, \indexit{291}
  `UseIsomorphismRelation', 290
  User Streams, \indexit{102}
  `UseSubsetRelation', 290
  utilities for editing GAP files, 73
\letter V
  $v_N$, 158
  `Valuation', 679
  `Value', 661
  `ValueCochain', 641
  `ValueGlobal', 43
  `ValueMolienSeries', 775
  `ValueOption', 87
  `ValuePol', 213
  `ValuesOfClassFunction', 752
  Variable Access in a Break Loop, \indexit{69}
  Variables, \indexit{41}
  Vectors as coefficients of polynomials, \indexit{213}
  `VectorSpace', 584
  `Vector\-Space\-By\-Pcgs\-Of\-Elementary\-Abelian\-Group', 439
  Vector Space Homomorphisms, \indexit{595}
  Vector Spaces Handled By Nice Bases, \indexit{597}
  `vi', 73
  `View', 64
  View and Print, \indexit{64}
  `ViewObj', 65
    \sub for character tables, 731
    \sub for class functions, 756
    \sub for tables of marks, 690
  `vim', 73
  `VirtualCharacter', 757
  virtual character, 759
  virtual characters, 750
\letter W
  $w_N$, 158
  `WedgeGModule ', 682
  `WeekDay', 252
  `WeightLexOrdering', 276
  `WeightOfGenerators', 277
  `WeightsTom', 696
  `WeightVecFFE', 212
  `WeylGroup', 633
  `WeylOrbitIterator', 635
  `Where', 69
  While, \indexit{50}
  `while' loop, 50
  Whitespaces, \indexit{39}
  Why Class Functions?, \indexit{750}
  `WordAlp', 247
  words, in generators, 345
  Working with large degree permutation groups, \indexit{417}
  `WreathProduct', 497
  wreath product embedding, 498
  `WreathProductImprimitiveAction', 497
  `WreathProductOrdering', 278
  `WreathProductProductAction', 498
  Wreath Products, \indexit{497}
  `WriteAll', 100
  `WriteByte', 100
  `WriteLine', 100
\letter X
  $x_N$, 158
\letter Y
  $y_N$, 158
\letter Z
  `Z', 572
  `ZClassRepsQClass', 424
  `Zero', 286
  `ZeroAttr', 286
  `ZeroCoefficient', 650
  `ZeroCoefficientRatFun', 674
  `ZeroImmutable', 286
  `ZeroMapping', 297
  `ZeroMutable', 286
  `ZeroOp', 286
  `ZeroSameMutability', 286
  `ZeroSM', 286
  `ZippedProduct', 675
  `ZippedSum', 675
  `ZmodnZ', 132
  `ZmodnZObj', 133
  `ZmodpZ', 132
  `ZmodpZNC', 132
  `ZumbroichBase', 580
  `Zuppos', 367
