# The GAP 4 Manual - Full Index I

_ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

i_N R 18.4
Ideal R 54.2.1
IdealByGenerators R 54.2.4
IdealNC R 54.2.2
Ideals R 60.6
Ideals in Rings R 54.2
Ideals of semigroups R 49.2
Idempotents R 33.4.6
IdempotentsTom R 68.7.8
IdempotentsTomInfo R 68.7.8
Identical Lists R 21.6
Identical Lists T 3.2
Identical Objects R 12.5
Identical Records R 27.3
IdentificationOfConjugacyClasses R 69.6.3
Identifier, for character tables R 69.8.11
Identifier, for tables of marks R 68.7.9
identifier T 2.5
Identifiers R 4.6
Identity R 30.10.2
IdentityBinaryRelation R 32.1.3
IdentityFromSCTable R 60.3.6
IdentityMapping R 31.1.9
IdentityMat R 24.4.1
IdentityTransformation R 52.0
IdFunc R 5.3.4
IdGap3SolvableGroup R 48.7.7
IdGroup R 48.7.5
IdSmallGroup R 48.7.5
IdsOfAllSmallGroups R 48.7.6
If R 4.16
if statement R 4.16.1
If Statements T 4.2
If Things Go Wrong R 73.9
Image R 31.3.6
Image, for Frobenius automorphisms R 57.4
image, vector under matrix R 24.2.10
ImageElm R 31.3.5
ImageElt N 3.2.3
ImageGroup N 4.3.4
ImageListOfTransformation R 52.0
Images R 31.3.7
Images under Mappings R 31.3
ImagesElm R 31.3.3
ImageSetOfTransformation R 52.0
ImagesRepresentative R 31.3.2
ImagesSet R 31.3.4
ImagesSmallestGenerators R 38.3.1
ImagesSource R 31.3.1
ImagesSource N 3.2.7
ImfInvariants R 48.12.3
ImfMatrixGroup R 48.12.4
ImfNumberQClasses R 48.12.1
ImfNumberQQClasses R 48.12.1
ImfNumberZClasses R 48.12.1
Immediate and True Methods T 8.3
Immediate Methods P 2.6
Immutability T 3.3
Immutable R 12.6.3
Immutable Objects T 9.6
ImmutableBasis R 59.7.4
ImmutableMatrix R 24.13.1
Implementing New List Objects P 3.11
in, for collections R 28.5.1
in, for lists R 21.8
in, for strictly sorted lists R 21.19.1
in, operation for R 28.5.1
In Parent Attributes E 6.2
IndependentGeneratorsOfAbelianGroup R 37.22.5
Indeterminate R 64.1.1
IndeterminateName R 64.1.4
Indeterminateness R 71.3.13
IndeterminateNumberOfLaurentPolynomial R 64.12.3
IndeterminateNumberOfUnivariateRationalFunction R 64.1.2
IndeterminateOfUnivariateRationalFunction R 64.1.3
Indeterminates R 64.1
IndeterminatesOfPolynomialRing R 64.14.2
Index R 37.3.2
Index numbers of primitive groups R 48.10
indexing commands E 2.5
IndexInWholeGroup R 37.3.3
IndexNC R 37.3.2
Indicator R 69.10.4
IndicatorOp R 69.10.4
IndicesCentralNormalSteps R 43.11.7
IndicesChiefNormalSteps R 43.11.15
IndicesEANormalSteps R 43.11.3
IndicesInvolutaryGenerators R 45.5.9
IndicesNormalSteps R 43.11.17
IndicesOfAdjointBasis R 60.8.6
IndicesPCentralNormalStepsPGroup R 43.11.11
IndicesStabChain R 41.9.7
Indirected R 71.3.4
Induced Actions R 67.7
InducedAutomorphism R 38.7.6
InducedClassFunction R 70.9.3
InducedClassFunctions R 70.9.4
InducedCyclic R 70.9.5
InducedPcgs R 43.7.4
InducedPcgsByGenerators R 43.7.5
InducedPcgsByGeneratorsNC R 43.7.5
InducedPcgsByPcSequence R 43.7.2
InducedPcgsByPcSequenceAndGenerators R 43.7.6
InducedPcgsByPcSequenceNC R 43.7.2
InducedPcgsWrtFamilyPcgs R 44.1.3
InducedPcgsWrtSpecialPcgs R 43.13.8
Inequalities R 70.14.5
inequality, of records R 27.4.1
inequality test R 4.11.1
InertiaSubgroup R 70.8.13
Infinity R 18.2
infinity R 18.2.1
inflated class functions R 70.9
Info R 7.4.5
Info Functions R 7.4
InfoAlgebra R 60.0
InfoAttributes R 13.6.4
InfoBckt R 41.11.4
InfoCharacterTable R 69.4.2
InfoCoh R 37.23.5
InfoComplement R 37.11.7
InfoCoset R 37.9.6
InfoFpGroup R 45.0
InfoGroebner R 64.17.4
InfoGroup R 37.2.7
InfoLattice R 37.20.8
InfoLevel R 7.4.4
InfoMatrix R 24.0
InfoMonomial R 72.0
InfoNumtheor R 15.0
InfoOptions R 8.0
InfoPcSubgroup R 37.21.6
Information about a function R 5.1
Information about the version used R 7.8
InfoText R 69.8.12
InfoTom R 68.6.1
InfoWarning R 7.4.6
init.g, for a GAP package E 4.7
InitFusion R 71.5.1
InitPowerMap R 71.4.1
Injection N 4.4.2
InjectionZeroMagma R 33.2.12
inner product, of group characters R 70.8
InnerAutomorphism R 38.6.3
InnerAutomorphismNC R 38.6.3
InnerAutomorphismsAutomorphismGroup R 38.7.5
InParentFOA E 6.2.1
Input-Output Streams R 10.8
InputLogTo R 9.7.7
InputLogTo, for streams R 10.4.6
InputLogTo, stop logging input R 9.7.8
InputOutputLocalProcess R 10.8.2
InputTextFile R 10.5.1
InputTextNone R 10.9.1
InputTextString R 10.7.1
InputTextUser R 10.6.1
InsertTrivialStabilizer R 41.10.8
InstallAtExit R 6.7.2
installation R 73.0
Installation of GAP for MacOS R 73.16
Installation of GAP Package Binaries E 4.9
Installation Overview R 73.1
InstallCharReadHookFunc R 10.10.1
InstalledPackageVersion R 74.3.3
InstallFactorMaintenance R 30.13.6
InstallFlushableValue P 3.17.6
InstallGlobalFunction P 3.17.4
InstallHandlingByNiceBasis R 59.11.1
InstallImmediateMethod P 2.6.1
Installing a GAP Package R 74.1
Installing a Help Book E 5.1
Installing GAP R 73.0
InstallIsomorphismMaintenance R 30.13.5
InstallMethod P 2.2.1
InstallOtherMethod P 2.2.2
InstallSubsetMaintenance R 30.13.4
InstallTrueMethod P 2.7.1
InstallValue P 3.17.6
Int R 14.1.3
Int, for cyclotomics R 18.1
Int, for strings R 26.7.1
INT_CHAR R 26.6.1
integer part of a quotient R 14.2
Integers R 14.0 R 14.0
Integral Bases of Abelian Number Fields R 58.3
Integral matrices and lattices R 25.0
IntegralizedMat R 25.4.4
IntegratedStraightLineProgram R 35.8.8
Interface to the GAP Help System E 5.0
IntermediateGroup R 37.17.17
IntermediateSubgroups R 37.17.18
Internally Represented Cyclotomics R 18.6
Internally Represented Strings R 26.2
InterpolatedPolynomial R 54.7.9
IntersectBlist R 22.3.3
Intersection R 28.4.2
Intersection, for groups with pcgs R 43.16
intersection, of collections R 28.4
intersection, of sets R 21.19
Intersection2 R 28.4.2
IntersectionBlist R 22.2.2
IntersectionsTom R 68.9.10
IntersectSet R 21.19.7
IntFFE R 57.2.3
IntFFESymm R 57.2.4
IntHexString R 26.7.1
Introducing new Viewer for the Online Help E 5.4
IntScalarProducts R 71.3.15 R 71.3
IntVecFFE R 57.2.5
Invariant Forms R 42.4 R 67.9
InvariantBilinearForm R 42.4.1
InvariantElementaryAbelianSeries R 37.17.10
InvariantLattice R 42.5.6
InvariantQuadraticForm R 42.4.5
InvariantSesquilinearForm R 42.4.3
InvariantSubgroupsElementaryAbelianGroup R 37.21.2
Inverse R 30.10.8
Inverse, group homomorphism R 38.2
inverse, matrix R 24.2.8
inverse, of class function R 70.4
InverseAttr R 30.10.8
InverseClasses R 69.8.13
InverseGeneralMapping R 31.1.3
InverseImmutable R 30.10.8
InverseMap R 71.3.2
InverseMatMod R 24.13.5
InverseMutable R 30.10.8
InverseOp R 30.10.8
InverseRepresentative R 41.9.10
InverseSameMutability R 30.10.8
InverseSM R 30.10.8
Invoking the Help R 2.1
Irr R 69.8.2
irrationalities R 18.0
IrrBaumClausen R 69.12.3
IrrConlon R 69.12.2
IrrDixonSchneider R 69.12.1
Irreducibility Tests R 67.5
irreducible character R 70.8
irreducible characters, computation R 69.15
Irreducible Maximal Finite Integral Matrix Groups R 48.12
Irreducible Solvable Matrix Groups R 48.11
IrreducibleDifferences R 70.10.3
IrreducibleModules R 69.13.1
IrreducibleModules, for groups with pcgs R 43.16
IrreducibleRepresentations R 69.12.4
IrreducibleRepresentationsDixon R 69.12.5
IrreducibleSolvableGroup R 48.11.6
IrreducibleSolvableGroupMS R 48.11.1
Is16BitsFamily R 35.6.7
Is32BitsFamily R 35.6.7
Is8BitsFamily R 35.6.7
IsAbelian R 33.4.9
IsAbelian, for character tables R 69.8
IsAbelianNumberField R 58.2.2
IsAbelianNumberFieldPolynomialRing R 64.14.6
IsAbelianTom R 68.8.1
IsAdditiveElement R 30.14.3
IsAdditiveElementWithInverse R 30.14.7
IsAdditiveElementWithZero R 30.14.5
IsAdditiveGroup R 53.1.6
IsAdditiveGroupGeneralMapping R 31.9.4
IsAdditiveGroupHomomorphism R 31.9.4
IsAdditivelyCommutative R 53.3.1
IsAdditivelyCommutativeElement R 30.15.2
IsAdditivelyCommutativeElementCollColl R 30.15.2
IsAdditivelyCommutativeElementCollection R 30.15.2
IsAdditivelyCommutativeElementFamily R 30.15.2
IsAdditiveMagma R 53.1.4
IsAdditiveMagmaWithInverses R 53.1.6
IsAdditiveMagmaWithZero R 53.1.5
IsAlgebra R 60.7.3
IsAlgebraGeneralMapping R 31.11.3
IsAlgebraHomomorphism R 31.11.3
IsAlgebraicElement R 65.2.1
IsAlgebraicExtension R 65.1.2
IsAlgebraModuleElement R 60.10.8
IsAlgebraModuleElementCollection R 60.10.8
IsAlgebraModuleElementFamily R 60.10.8
IsAlgebraWithOne R 60.7.4
IsAlgebraWithOneGeneralMapping R 31.11.4
IsAlgebraWithOneHomomorphism R 31.11.4
IsAlphaChar R 26.3.4
IsAlternatingGroup R 41.3.4
IsAnticommutative R 54.4.6
IsAntisymmetricBinaryRelation R 32.2.4
IsAssociated R 54.5.3
IsAssociative R 33.4.7
IsAssociativeElement R 30.15.1
IsAssociativeElementCollColl R 30.15.1
IsAssociativeElementCollection R 30.15.1
IsAssocWord R 35.1.1
IsAssocWordWithInverse R 35.1.1
IsAssocWordWithOne R 35.1.1
IsAttributeStoringRep P 4.5 P 4.6
IsAutomorphismGroup R 38.7.4
IsBasicWreathLessThanOrEqual R 35.3.4
IsBasicWreathProductOrdering R 29.3.12
IsBasis R 59.4.1
IsBasisByNiceBasis R 59.10.5
IsBasisOfAlgebraModuleElementSpace R 60.10.14
IsBergerCondition R 72.1.3
IsBijection T 9.4
IsBijective R 31.2.6
IsBinaryRelation R 32.1.1
IsBinaryRelation, same as IsEndoGeneralMapping R 32.0
IsBLetterAssocWordRep R 35.6.3
IsBLetterWordsFamily R 35.6.4
IsBlist R 22.0
IsBlockMatrixRep R 24.15
IsBool R 20.0
IsBound, for lists R 21.5.1
IsBound and Unbind for Lists R 21.5
IsBound and Unbind for Records R 27.5
IsBOundElmWPObj E 7.3.1
IsBoundGlobal R 4.9.5
IsBrauerTable R 69.4.1
IsBravaisGroup R 42.5.10
IsBuiltFromAdditiveMagmaWithInverses R 36.3.1
IsBuiltFromGroup R 36.3.6
IsBuiltFromMagma R 36.3.2
IsBuiltFromMagmaWithInverses R 36.3.4
IsBuiltFromMagmaWithOne R 36.3.3
IsBuiltFromSemigroup R 36.3.5
IsCanonicalBasis R 59.6.1
IsCanonicalBasisFullMatrixModule R 59.8.10
IsCanonicalBasisFullRowModule R 59.8.9
IsCanonicalNiceMonomorphism R 38.5.4
IsCanonicalPcgs R 43.8.1
IsCentral R 33.4.8
IsChainTypeGroup N 5.0
IsChar R 26.0
IsCharacter R 70.8.1
IsCharacteristicSubgroup R 37.3.7
IsCharacterTable R 69.4.1
IsCharacterTableInProgress R 69.4.1
IsCharCollection R 26.0
IsCheapConwayPolynomial R 57.5.2
IsClassFunction R 70.0
IsClassFusionOfNormalSubgroup R 69.10.3
IsClosedStream R 10.1.2
IsCochain R 61.12.2
IsCochainCollection R 61.12.2
IsCollection R 28.0
IsCollectionFamily R 28.1.2
IsCommutative R 33.4.9
IsCommutativeElement R 30.15.3
IsCommutativeElementCollColl R 30.15.3
IsCommutativeElementCollection R 30.15.3
IsComponentObjectRep P 4.6
IsCompositionMappingRep R 31.1.6
IsConfluent R 36.1.5
IsConfluent, for pc groups R 44.4.7
IsConjugacyClassSubgroupsByStabilizerRep R 37.19.2
IsConjugacyClassSubgroupsRep R 37.19.2
IsConjugate R 37.10.9
IsConjugatorAutomorphism R 38.6.4
IsConjugatorIsomorphism R 38.6.4
IsConstantRationalFunction R 64.4.11
IsConstantTimeAccessGeneralMapping R 31.12.2
IsConstantTimeAccessList R 21.1.5
IsContainedInSpan R 59.7.5
IsCopyable R 12.6.1
IsCyc R 18.1.3
IsCyclic R 37.15.1
IsCyclic, for character tables R 69.8
IsCyclicTom R 68.8.1
IsCyclotomic R 18.1.3
IsCyclotomicField R 58.2.3
IsCyclotomicMatrixGroup R 42.5.1
IsDenseList R 21.1.2
IsDiagonalMat R 24.3.8
IsDictionary N 2.1.1
IsDigitChar R 26.3.1
IsDirectoryPath R 9.6.5
IsDistributive R 54.4.5
IsDivisionRing R 56.1.1
IsDomain R 30.9.1
IsDoneIterator R 28.7.4
IsDoubleCoset R 37.9.4
IsDuplicateFree R 21.17.2
IsDuplicateFreeList R 21.17.2
IsDxLargeGroup R 69.15.8
IsElementaryAbelian R 37.15.2
IsElementaryAbelian, for character tables R 69.8
IsElementOfFpMonoid R 51.0
IsElementOfFpSemigroup R 51.0
IsElementOfFreeMagmaRing R 63.2.1
IsElementOfFreeMagmaRingCollection R 63.2.1
IsElementOfFreeMagmaRingFamily R 63.2.2
IsElementOfMagmaRingModuloRelations R 63.4.1
IsElementOfMagmaRingModuloRelationsCollection R 63.4.1
IsElementOfMagmaRingModuloRelationsFamily R 63.4.2
IsElementOfMagmaRingModuloSpanOfZeroFamily R 63.5.1
IsEmpty R 28.3.1
IsEmptyString R 26.2.3
IsEndOfStream R 10.3.7
IsEndoGeneralMapping R 31.12.3
IsEndoGeneralMapping, same as IsBinaryRelation R 32.0
IsEqualSet R 21.19.2
IsEquivalenceClass R 32.7.1
IsEquivalenceRelation R 32.2.8
IsEuclideanRing R 54.6.1
IsEvenInt R 14.1.4
IsExecutableFile R 9.6.4
IsExistingFile R 9.6.1
IsExtAElement R 30.14.1
IsExternalOrbit R 39.11.8
IsExternalSet R 39.11.1
IsExternalSubset R 39.11.6
IsExtLElement R 30.14.8
IsExtRElement R 30.14.9
IsFamilyPcgs R 44.1.2
IsFFE R 57.1.1
IsFFECollColl R 57.1.1
IsFFECollection R 57.1.1
IsField R 56.1.2
IsFieldControlledByGaloisGroup R 56.3
IsFieldHomomorphism R 31.11.5
IsFinite R 28.3.2
IsFinite, for character tables R 69.8
IsFiniteDimensional R 55.3.5
IsFiniteDimensional, for matrix algebras R 60.7.7
IsFiniteFieldPolynomialRing R 64.14.5
IsFinitelyGeneratedGroup R 37.15.12
IsFiniteOrderElement R 30.15.4
IsFiniteOrderElementCollColl R 30.15.4
IsFiniteOrderElementCollection R 30.15.4
IsFiniteOrdersPcgs R 43.4.2
IsFixedStabilizer R 41.10.9
IsFLMLOR R 60.7.1
IsFLMLORWithOne R 60.7.2
IsFpGroup R 45.0
IsFpMonoid R 51.0
IsFpSemigroup R 51.0
IsFreeGroup R 35.2.2
IsFreeLeftModule R 55.3.1
IsFreeMagmaRing R 63.1.3
IsFreeMagmaRingWithOne R 63.1.4
IsFromFpGroupGeneralMappingByImages R 38.10.9
IsFromFpGroupHomomorphismByImages R 38.10.9
IsFromFpGroupStdGensGeneralMappingByImages R 38.10.10
IsFromFpGroupStdGensHomomorphismByImages R 38.10.10
IsFullHomModule R 59.9.7
IsFullMatrixModule R 55.3.11
IsFullRowModule R 55.3.9
IsFullSubgroupGLorSLRespectingBilinearForm R 42.4.2
IsFullSubgroupGLorSLRespectingQuadraticForm R 42.4.6
IsFullSubgroupGLorSLRespectingSesquilinearForm R 42.4.4
IsFullTransformationSemigroup R 49.1.4
IsFunc T 9.4
IsFunction R 5.4.1
IsGaussianIntegers R 58.5.2
IsGaussianRationals R 58.1.3
IsGaussianSpace R 59.8.3
IsGaussInt R 18.1.12
IsGaussRat R 18.1.13
IsGeneralizedDomain R 30.9.1
IsGeneralizedRowVector R 21.12.1
IsGeneralLinearGroup R 42.3.1
IsGeneralMapping R 31.12.1
IsGeneralMappingFamily R 31.13.2
IsGeneratorsOfStruct R 30.3.2
IsGL R 42.3.1
IsGreensClass R 49.5.3
IsGreensDClass R 49.5.3
IsGreensDRelation R 49.5.2
IsGreensHClass R 49.5.3
IsGreensHRelation R 49.5.2
IsGreensJClass R 49.5.3
IsGreensJRelation R 49.5.2
IsGreensLClass R 49.5.3
IsGreensLessThanOrEqual R 49.5.4
IsGreensLRelation R 49.5.2
IsGreensRClass R 49.5.3
IsGreensRelation R 49.5.2
IsGreensRRelation R 49.5.2
IsGroup R 37.2.6
IsGroupGeneralMapping R 31.8.4
IsGroupGeneralMappingByAsGroupGeneralMappingByImages R 38.10.2
IsGroupGeneralMappingByImages R 38.10.1
IsGroupGeneralMappingByPcgs R 38.10.6
IsGroupHClass R 49.5.11
IsGroupHomomorphism R 31.8.4
IsGroupOfAutomorphisms R 38.7.1
IsGroupRing R 63.1.5
IsHandledByNiceBasis R 55.3.13
IsHandledByNiceBasis, for vector spaces R 59.10.6
IsHandledByNiceMonomorphism R 38.5.1
IsHash N 2.3.1
IsHasseDiagram R 32.2.7
IsHomCoset N 3.0
IsHomCosetOfAdditiveElt N 3.0
IsHomCosetOfFp N 3.0
IsHomCosetOfMatrix N 3.0
IsHomCosetOfPerm N 3.0
IsHomCosetOfTuple N 3.0
IsHomCosetToAdditiveElt N 3.0
IsHomCosetToAdditiveEltRep N 3.0
IsHomCosetToFp N 3.0
IsHomCosetToFpRep N 3.0
IsHomCosetToMatrix N 3.0
IsHomCosetToMatrixRep N 3.0
IsHomCosetToObjectRep N 3.0
IsHomCosetToPerm N 3.0
IsHomCosetToPermRep N 3.0
IsHomCosetToTuple N 3.0
IsHomCosetToTupleRep N 3.0
IsHomogeneousList R 21.1.3
IsIdempotent R 30.10.7
IsIdenticalObj R 12.5.1
IsIdenticalObj T 2.6
IsInChain N 5.0
IsIncomparableUnder R 29.2.3
IsInducedFromNormalSubgroup R 72.2.4
IsInducedPcgs R 43.7.1
IsInducedPcgsWrtSpecialPcgs R 43.13.7
IsInfBitsFamily R 35.6.7
IsInfinity R 18.2.1
IsInjective R 31.2.4
IsInnerAutomorphism R 38.6.4
IsInputOutputStream R 10.8.1
IsInputStream R 10.1.3
IsInputTextNone R 10.1.5
IsInputTextStream R 10.1.4
IsInt R 14.1.1
IsIntegerMatrixGroup R 42.5.3
IsIntegers R 14.0
IsIntegralBasis R 59.6.2
IsIntegralCyclotomic R 18.1.4
IsIntegralRing R 54.4.1
IsInternallyConsistent R 12.8.3
IsInternallyConsistent, for character tables R 69.10.1
IsInternallyConsistent, for tables of marks R 68.9.1
IsIrreducibleCharacter R 70.8.3
IsIrreducibleRingElement R 54.5.6
IsIterator R 28.7.3
IsJacobianElement R 30.15.5
IsJacobianElementCollColl R 30.15.5
IsJacobianElementCollection R 30.15.5
IsJacobianRing R 54.4.8
IsLaurentPolynomial R 64.4.10
IsLaurentPolynomialDefaultRep R 64.20.7
IsLDistributive R 54.4.3
IsLeftAlgebraModuleElement R 60.10.9
IsLeftAlgebraModuleElementCollection R 60.10.9
IsLeftIdeal R 54.2.3
IsLeftIdealInParent R 54.2.3
IsLeftModule R 55.1.2
IsLeftModuleGeneralMapping R 31.10.2
IsLeftModuleHomomorphism R 31.10.2
IsLeftOperatorAdditiveGroup R 55.1.1
IsLeftSemigroupIdeal R 49.2.3
IsLeftVectorSpace R 59.0
IsLessThanOrEqualUnder R 29.2.8
IsLessThanUnder R 29.2.7
IsLetterAssocWordRep R 35.6.1
IsLetterWordsFamily R 35.6.2
IsLexicographicallyLess R 21.20.8
IsLieAbelian R 61.5.1
IsLieAlgebra R 60.7.5
IsLieMatrix R 24.1.3
IsLieNilpotent R 61.5.2
IsLieObject R 61.1.2
IsLieObjectCollection R 61.1.2
IsLieSolvable R 61.5.3
IsLinearMapping R 31.10.3
IsLinearMappingsModule R 59.9.9
IsList R 21.1.1
IsListDefault R 21.12.3
IsListOrCollection R 28.2.1
IsLookupDictionary N 2.1.2
IsLowerAlphaChar R 26.3.2
IsLowerTriangularMat R 24.3.10
IsMagma R 33.1.1
IsMagmaHomomorphism R 31.7.1
IsMagmaRingModuloRelations R 63.4.4
IsMagmaRingModuloSpanOfZero R 63.5.2
IsMagmaWithInverses R 33.1.4
IsMagmaWithInversesIfNonzero R 33.1.3
IsMagmaWithOne R 33.1.2
IsMapping R 31.2.3
IsMat T 9.4
IsMatchingSublist R 21.17.1
IsMatrix R 24.1.1
IsMatrixGroup R 42.0
IsMatrixModule R 55.3.8
IsMatrixSpace R 59.8.2
IsMinimalNonmonomial R 72.4.1
IsModuloPcgs R 43.9.2
IsMonoid R 50.0
IsMonomial, for character tables R 69.8
IsMonomial, for characters R 72.3
IsMonomial, for groups R 72.3
IsMonomial, for positive integers R 72.3
IsMonomialGroup R 37.15.9
IsMonomialMatrix R 24.3.7
IsMonomialNumber R 72.3.3
IsMonomialOrdering R 64.16.1
IsMultiplicativeElement R 30.14.10
IsMultiplicativeElementWithInverse R 30.14.13
IsMultiplicativeElementWithOne R 30.14.11
IsMultiplicativeElementWithZero R 30.14.12
IsMultiplicativeGeneralizedRowVector R 21.12.2
IsMultiplicativeZero R 33.4.12
IsMutable R 12.6.2
IsMutableBasis R 59.7.1
IsNaturalAlternatingGroup R 41.3.2
IsNaturalGL R 42.3.2
IsNaturalGLnZ R 42.5.4
IsNaturalSL R 42.3.4
IsNaturalSLnZ R 42.5.5
IsNaturalSymmetricGroup R 41.3.1
IsNearAdditiveElement R 30.14.2
IsNearAdditiveElementWithInverse R 30.14.6
IsNearAdditiveElementWithZero R 30.14.4
IsNearAdditiveGroup R 53.1.3
IsNearAdditiveMagma R 53.1.1
IsNearAdditiveMagmaWithInverses R 53.1.3
IsNearAdditiveMagmaWithZero R 53.1.2
IsNearlyCharacterTable R 69.4.1
IsNearRingElement R 30.14.15
IsNearRingElementWithInverse R 30.14.19
IsNearRingElementWithOne R 30.14.17
IsNegRat R 16.1.3
IsNilpotent, for character tables R 69.8
IsNilpotent, for groups with pcgs R 43.16
IsNilpotentElement R 61.9.5
IsNilpotentGroup R 37.15.3
IsNilpotentTom R 68.8.1
IsNonassocWord R 34.1.3
IsNonassocWordCollection R 34.1.4
IsNonassocWordWithOne R 34.1.3
IsNonassocWordWithOneCollection R 34.1.4
IsNonnegativeIntegers R 14.0
IsNonSPGeneralMapping R 31.13.1
IsNonTrivial R 28.3.4
IsNormal R 37.3.6
IsNormalBasis R 59.6.3
IsNotIdenticalObj R 12.5.2
IsNumberField R 58.2.1
IsObject R 12.1.1
IsOddInt R 14.1.5
isomorphic, pc group R 44.4 R 44.5
IsomorphicSubgroups R 38.9.3
IsomorphismFpAlgebra R 60.9.9
IsomorphismFpGroup R 45.10.1
IsomorphismFpGroup, for subgroups of fp groups R 45.11
IsomorphismFpGroupByGenerators R 45.10.2
IsomorphismFpGroupByGeneratorsNC R 45.10.2
IsomorphismFpGroupByPcgs R 44.3.2
IsomorphismFpSemigroup R 51.1.3
IsomorphismGroups R 38.9.1
IsomorphismMatrixAlgebra R 60.9.10
IsomorphismPcGroup R 44.5.2
IsomorphismPermGroup R 41.2.1
IsomorphismPermGroup, for Imf matrix groups R 48.12.5
IsomorphismPermGroupImfGroup R 48.12.6
IsomorphismReesMatrixSemigroup R 49.6.11
IsomorphismRefinedPcGroup R 44.4.8
IsomorphismRepStruct R 30.5.1
isomorphisms, find all R 38.9
Isomorphisms vs. Isomorphic Structures T 9.15
IsomorphismSCAlgebra R 60.9.11
IsomorphismSimplifiedFpGroup R 45.11.1
IsomorphismSpecialPcGroup R 44.5.3
IsomorphismTransformationSemigroup R 49.1.3
IsomorphismTypeInfoFiniteSimpleGroup R 37.15.11
IsOne R 30.10.5
IsOperation R 5.4.2
IsOrdering R 29.0
IsOrderingOnFamilyOfAssocWords R 29.3.1
IsOrdinaryMatrix R 24.1.2
IsOrdinaryTable R 69.4.1
IsOutputStream R 10.1.6
IsOutputTextNone R 10.1.8
IsOutputTextStream R 10.1.7
IsPadicExtensionNumber R 66.2.3
IsPadicExtensionNumberFamily R 66.2.4
IsParentPcgsFamilyPcgs R 44.1.4
IsPartialOrderBinaryRelation R 32.2.6
IsPcGroup R 44.3.1
IsPcGroupGeneralMappingByImages R 38.10.7
IsPcGroupHomomorphismByImages R 38.10.7
IsPcgs R 43.2.2
IsPcgsCentralSeries R 43.11.5
IsPcgsChiefSeries R 43.11.13
IsPcgsElementaryAbelianSeries R 43.11.1
IsPcgsPCentralSeriesPGroup R 43.11.9
IsPerfect, for character tables R 69.8
IsPerfectGroup R 37.15.5
IsPerfectTom R 68.8.1
IsPerm R 40.0
IsPermCollColl R 40.0
IsPermCollection R 40.0
IsPermGroup R 41.0
IsPermGroupGeneralMappingByImages R 38.10.4
IsPermGroupHomomorphismByImages R 38.10.4
IsPGroup R 37.15.14
IsPNilpotent R 37.15.19
IsPolycyclicGroup R 37.15.7
IsPolynomial R 64.4.4
IsPolynomialDefaultRep R 64.20.5
IsPolynomialFunction R 64.4.1
IsPolynomialFunctionsFamily R 64.18.2
IsPolynomialRing R 64.14.4
IsPosInt R 14.1.2
IsPositiveIntegers R 14.0
IsPosRat R 16.1.2
IsPreimagesByAsGroupGeneralMappingByImages R 38.10.3
IsPreOrderBinaryRelation R 32.2.5
IsPrime R 54.5.7
IsPrimeField R 56.2.5
IsPrimeInt R 14.3.2
IsPrimeOrdersPcgs R 43.4.3
IsPrimePowerInt R 14.3.3
IsPrimitive R 39.9.7
IsPrimitiveCharacter R 72.2.2
IsPrimitivePolynomial R 64.4.12
IsPrimitiveRootMod R 15.2.4
IsProbablyPrimeInt R 14.3.2
IsPseudoCanonicalBasisFullHomModule R 59.9.8
IsPSolvable R 37.15.18
IsPSolvableCharacterTable R 69.10.2
IsPSolvableCharacterTableOp R 69.10.2
IsPurePadicNumber R 66.1.5
IsPurePadicNumberFamily R 66.1.6
IsQuasiPrimitive R 72.2.3
IsQuaternion R 60.7.8
IsQuaternionCollColl R 60.7.8
IsQuaternionCollection R 60.7.8
IsQuickPositionList R 21.23.1
IsQuotientSemigroup R 49.4.1
IsRange R 21.22.1
IsRat R 16.1.1
IsRationalFunction R 64.4.1
IsRationalFunctionDefaultRep R 64.20.1
IsRationalFunctionsFamily R 64.18.2
IsRationalMatrixGroup R 42.5.2
IsRationals R 16.0
IsRationalsPolynomialRing R 64.14.7
IsRDistributive R 54.4.4
IsReadableFile R 9.6.2
IsReadOnlyGlobal R 4.9.1
IsRec T 9.4
IsRecord R 27.0
IsRecordCollColl R 27.0
IsRecordCollection R 27.0
IsReduced R 36.1.7
IsReductionOrdering R 29.3.3
IsReesCongruence R 49.3.2
IsReesCongruenceSemigroup R 49.0
IsReesMatrixSemigroup R 49.6.3
IsReesMatrixSemigroupElement R 49.6.6
IsReesZeroMatrixSemigroup R 49.6.4
IsReesZeroMatrixSemigroupElement R 49.6.6
IsReflexiveBinaryRelation R 32.2.1
IsRegular R 39.9.5
IsRegularDClass R 49.5.12
IsRegularSemigroup R 49.0
IsRegularSemigroupElement R 49.0
IsRelativelySM R 72.3.6
IsRestrictedLieAlgebra R 61.8.1
IsRewritingSystem R 36.1.1
IsRightAlgebraModuleElement R 60.10.10
IsRightAlgebraModuleElementCollection R 60.10.10
IsRightCoset R 37.7.4
IsRightIdeal R 54.2.3
IsRightIdealInParent R 54.2.3
IsRightModule R 55.1.7
IsRightOperatorAdditiveGroup R 55.1.6
IsRightSemigroupIdeal R 49.2.3
IsRing R 54.1.1
IsRingElement R 30.14.16
IsRingElementWithInverse R 30.14.20
IsRingElementWithOne R 30.14.18
IsRingGeneralMapping R 31.11.1
IsRingHomomorphism R 31.11.1
IsRingWithOne R 54.3.1
IsRingWithOneGeneralMapping R 31.11.2
IsRingWithOneHomomorphism R 31.11.2
IsRootSystem R 61.7.3
IsRootSystemFromLieAlgebra R 61.7.4
IsRowModule R 55.3.7
IsRowSpace R 59.8.1
IsRowVector R 23.0
IsScalar R 30.14.20
IsSemiEchelonized R 59.8.7
IsSemigroup R 49.0
IsSemigroupCongruence R 49.3.1
IsSemigroupIdeal R 49.2.3
IsSemiRegular R 39.9.4
IsSet R 21.17.4
IsSet T 9.4
IsShortLexLessThanOrEqual R 35.3.3
IsShortLexOrdering R 29.3.7
IsSimple, for character tables R 69.8
IsSimpleAlgebra R 60.7.6
IsSimpleGroup R 37.15.10
IsSimpleSemigroup R 49.0
IsSingleValued R 31.2.2
IsSL R 42.3.3
IsSolvable, for character tables R 69.8
IsSolvableGroup R 37.15.6
IsSolvableTom R 68.8.1
IsSortedList R 21.17.3
IsSpecialLinearGroup R 42.3.3
IsSpecialPcgs R 43.13.1
IsSPGeneralMapping R 31.13.1
IsSporadicSimple, for character tables R 69.8
IsSSortedList R 21.17.4
IsStandardGeneratorsOfGroup R 68.10.4
IsStraightLineProgElm R 35.9.1
IsStraightLineProgram R 35.8.1
IsStream R 10.1.1
IsString R 26.0
IsStringRep R 26.2.1
IsStruct R 30.6.1
IsSubgroup R 37.3.5
IsSubgroupFpGroup R 45.0
IsSubgroupOfWholeGroupByQuotientRep R 45.12.2
IsSubgroupSL R 42.3.5
IsSubmonoidFpMonoid R 51.0
IsSubnormal R 37.3.10
IsSubnormallyMonomial R 72.3.5
IsSubsemigroupFpSemigroup R 51.0
IsSubset R 28.4.1
IsSubsetBlist R 22.1.4
IsSubsetLocallyFiniteGroup R 37.15.13
IsSubsetSet R 21.19.3
IsSubspacesVectorSpace R 59.3.2
IsSubstruct R 30.8.4
IsSupersolvable, for character tables R 69.8
IsSupersolvable, for groups with pcgs R 43.16
IsSupersolvableGroup R 37.15.8
IsSurjective R 31.2.5
IsSyllableAssocWordRep R 35.6.5
IsSyllableWordsFamily R 35.6.6
IsSymmetricBinaryRelation R 32.2.2
IsSymmetricGroup R 41.3.3
IsTable R 21.1.4
IsTableOfMarks R 68.6.2
IsTableOfMarksWithGens R 68.11.3
IsToPcGroupGeneralMappingByImages R 38.10.8
IsToPcGroupHomomorphismByImages R 38.10.8
IsToPermGroupGeneralMappingByImages R 38.10.5
IsToPermGroupHomomorphismByImages R 38.10.5
IsTotal R 31.2.1
IsTotalOrdering R 29.2.2
IsTransformation R 52.0
IsTransformationCollection R 52.0
IsTransformationMonoid R 49.1.1
IsTransformationSemigroup R 49.1.1
IsTransitive, for characters R 70.8.15
IsTransitive, for class functions R 70.8
IsTransitive, for group actions R 39.9.1
IsTransitiveBinaryRelation R 32.2.3
IsTranslationInvariantOrdering R 29.3.2
IsTrivial R 28.3.3
IsTuple R 31.0
IsTwoSidedIdeal R 54.2.3
IsTwoSidedIdealInParent R 54.2.3
IsUEALatticeElement R 61.13.5
IsUEALatticeElementCollection R 61.13.5
IsUEALatticeElementFamily R 61.13.5
IsUniqueFactorizationRing R 54.4.2
IsUnit R 54.5.1
IsUnivariatePolynomial R 64.4.8
IsUnivariatePolynomialRing R 64.15.2
IsUnivariateRationalFunction R 64.4.6
IsUnknown R 19.0
IsUpperAlphaChar R 26.3.3
IsUpperTriangularMat R 24.3.9
IsValidIdentifier R 4.6.1
IsVector R 30.14.14
IsVectorSpace R 59.0
IsVirtualCharacter R 70.8.2
IsWeightLexOrdering R 29.3.9
IsWeightRepElement R 61.13.8
IsWeightRepElementCollection R 61.13.8
IsWeightRepElementFamily R 61.13.8
IsWellFoundedOrdering R 29.2.1
IsWeylGroup R 61.7.15
IsWholeFamily R 28.3.5
IsWLetterAssocWordRep R 35.6.3
IsWLetterWordsFamily R 35.6.4
IsWord R 34.1.1
IsWordCollection R 34.1.2
IsWordWithInverse R 34.1.1
IsWordWithOne R 34.1.1
IsWreathProductOrdering R 29.3.14
IsWritableFile R 9.6.3
IsZero R 30.10.6
IsZeroGroup R 49.0
IsZeroSimpleSemigroup R 49.0
IsZeroSquaredElement R 30.15.6
IsZeroSquaredElementCollColl R 30.15.6
IsZeroSquaredElementCollection R 30.15.6
IsZeroSquaredRing R 54.4.7
IsZmodnZObj R 14.4.4
IsZmodnZObjNonprime R 14.4.4
IsZmodpZObj R 14.4.4
IsZmodpZObjLarge R 14.4.4
IsZmodpZObjSmall R 14.4.4
Iterated R 21.20.25
Iterator R 28.7.1
IteratorByBasis R 59.5.6
IteratorByFunctions R 28.7.8
IteratorList R 28.7.6
Iterators R 28.7
IteratorSorted R 28.7.2

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