# The GAP 4 Reference Manual - 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 18.4
Ideal 54.2.1
IdealByGenerators 54.2.4
IdealNC 54.2.2
Ideals 60.6
Ideals in Rings 54.2
Ideals of semigroups 49.2
Idempotents 33.4.6
IdempotentsTom 68.7.8
IdempotentsTomInfo 68.7.8
Identical Lists 21.6
Identical Objects 12.5
Identical Records 27.3
IdentificationOfConjugacyClasses 69.6.3
Identifier, for character tables 69.8.12
Identifier, for tables of marks 68.7.9
Identifiers 4.6
Identity 30.10.2
IdentityBinaryRelation 32.1.3
IdentityFromSCTable 60.3.6
IdentityMapping 31.1.9
IdentityMat 24.4.1
IdentityTransformation 52.0
IdFunc 5.3.4
IdGap3SolvableGroup 48.7.7
IdGroup 48.7.5
IdSmallGroup 48.7.5
IdsOfAllSmallGroups 48.7.6
If 4.16
if statement 4.16.1
If Things Go Wrong 73.9
Image 31.3.6
Image, for Frobenius automorphisms 57.4
image, vector under matrix 24.2.10
ImageElm 31.3.5
ImageListOfTransformation 52.0
Images 31.3.7
Images under Mappings 31.3
ImagesElm 31.3.3
ImageSetOfTransformation 52.0
ImagesRepresentative 31.3.2
ImagesSet 31.3.4
ImagesSmallestGenerators 38.3.1
ImagesSource 31.3.1
ImaginaryPart 18.5.2
ImfInvariants 48.12.3
ImfMatrixGroup 48.12.4
ImfNumberQClasses 48.12.1
ImfNumberQQClasses 48.12.1
ImfNumberZClasses 48.12.1
Immutable 12.6.3
ImmutableBasis 59.7.4
ImmutableMatrix 24.13.1
in, for collections 28.5.1
in, for lists 21.8
in, for strictly sorted lists 21.19.1
in, operation for 28.5.1
IndependentGeneratorsOfAbelianGroup 37.22.5
Indeterminate 64.1.1
IndeterminateName 64.1.4
Indeterminateness 71.3.13
IndeterminateNumberOfLaurentPolynomial 64.12.3
IndeterminateNumberOfUnivariateRationalFunction 64.1.2
IndeterminateOfUnivariateRationalFunction 64.1.3
Indeterminates 64.1
IndeterminatesOfPolynomialRing 64.14.2
Index 37.3.2
Index numbers of primitive groups 48.10
IndexInWholeGroup 37.3.3
IndexNC 37.3.2
Indicator 69.10.4
IndicatorOp 69.10.4
IndicesCentralNormalSteps 43.11.7
IndicesChiefNormalSteps 43.11.15
IndicesEANormalSteps 43.11.3
IndicesInvolutaryGenerators 45.5.9
IndicesNormalSteps 43.11.17
IndicesOfAdjointBasis 60.8.6
IndicesPCentralNormalStepsPGroup 43.11.11
IndicesStabChain 41.9.7
Indirected 71.3.4
Induced Actions 67.7
InducedAutomorphism 38.7.6
InducedClassFunction 70.9.3
InducedClassFunctions 70.9.4
InducedClassFunctionsByFusionMap 70.9.5
InducedCyclic 70.9.6
InducedPcgs 43.7.4
InducedPcgsByGenerators 43.7.5
InducedPcgsByGeneratorsNC 43.7.5
InducedPcgsByPcSequence 43.7.2
InducedPcgsByPcSequenceAndGenerators 43.7.6
InducedPcgsByPcSequenceNC 43.7.2
InducedPcgsWrtFamilyPcgs 44.1.3
InducedPcgsWrtSpecialPcgs 43.13.8
Inequalities 70.14.5
inequality test 4.11.1
inequality, of records 27.4.1
InertiaSubgroup 70.8.13
Infinity 18.2
infinity 18.2.1
inflated class functions 70.9
Info 7.4.5
Info Functions 7.4
InfoAlgebra 60.0
InfoAttributes 13.6.4
InfoBckt 41.11.4
InfoCharacterTable 69.4.2
InfoCoh 37.23.5
InfoComplement 37.11.7
InfoCoset 37.9.6
InfoFpGroup 45.0
InfoGroebner 64.17.4
InfoGroup 37.2.7
InfoLattice 37.20.8
InfoLevel 7.4.4
InfoMatrix 24.0
InfoMonomial 72.0
InfoNumtheor 15.0
InfoOptions 8.0
InfoPcSubgroup 37.21.6
Information about a function 5.1
Information about the version used 7.8
InfoText 69.8.13
InfoTom 68.6.1
InfoWarning 7.4.6
Init 14.5.3
InitFusion 71.5.1
InitPowerMap 71.4.1
InjectionZeroMagma 33.2.12
inner product, of group characters 70.8
InnerAutomorphism 38.6.3
InnerAutomorphismNC 38.6.3
InnerAutomorphismsAutomorphismGroup 38.7.5
Input-Output Streams 10.8
InputLogTo 9.7.7
InputLogTo, for streams 10.4.6
InputLogTo, stop logging input 9.7.8
InputOutputLocalProcess 10.8.2
InputTextFile 10.5.1
InputTextNone 10.9.1
InputTextString 10.7.1
InputTextUser 10.6.1
InsertTrivialStabilizer 41.10.8
InstallAtExit 6.8.2
installation 73.0
Installation of GAP for MacOS 73.16
Installation Overview 73.1
InstallCharReadHookFunc 10.10.1
InstalledPackageVersion 74.3.3
InstallFactorMaintenance 30.13.6
InstallHandlingByNiceBasis 59.11.1
Installing a GAP Package 74.1
Installing GAP 73.0
InstallIsomorphismMaintenance 30.13.5
InstallSubsetMaintenance 30.13.4
Int 14.1.3
Int, for cyclotomics 18.1
Int, for strings 26.7.1
INT_CHAR 26.6.1
integer part of a quotient 14.2
Integers 14.0 14.0
Integral Bases of Abelian Number Fields 58.3
Integral matrices and lattices 25.0
IntegralizedMat 25.4.4
IntegratedStraightLineProgram 35.8.8
IntermediateGroup 37.17.17
IntermediateResultOfSLP 35.8.10
IntermediateResultOfSLPWithoutOverwrite 35.8.11
IntermediateResultsOfSLPWithoutOverwrite 35.8.12
IntermediateSubgroups 37.17.18
Internally Represented Cyclotomics 18.6
Internally Represented Strings 26.2
InterpolatedPolynomial 54.7.9
IntersectBlist 22.3.3
Intersection 28.4.2
Intersection, for groups with pcgs 43.16
intersection, of collections 28.4
intersection, of sets 21.19
Intersection2 28.4.2
IntersectionBlist 22.2.2
IntersectionsTom 68.9.10
IntersectSet 21.19.7
IntFFE 57.2.3
IntFFESymm 57.2.4
IntHexString 26.7.1
IntScalarProducts 71.3.15 71.3
IntVecFFE 57.2.5
Invariant Forms 42.4 67.9
InvariantBilinearForm 42.4.1
InvariantElementaryAbelianSeries 37.17.10
InvariantLattice 42.5.6
InvariantQuadraticForm 42.4.5
InvariantSesquilinearForm 42.4.3
InvariantSubgroupsElementaryAbelianGroup 37.21.2
Inverse 30.10.8
Inverse, group homomorphism 38.2
inverse, matrix 24.2.8
inverse, of class function 70.4
InverseAttr 30.10.8
InverseClasses 69.8.14
InverseGeneralMapping 31.1.3
InverseImmutable 30.10.8
InverseMap 71.3.2
InverseMatMod 24.13.5
InverseMutable 30.10.8
InverseOp 30.10.8
InverseRepresentative 41.9.10
InverseSameMutability 30.10.8
InverseSM 30.10.8
Invoking the Help 2.1
Irr 69.8.2
irrationalities 18.0
IrrBaumClausen 69.12.3
IrrConlon 69.12.2
IrrDixonSchneider 69.12.1
Irreducibility Tests 67.5
irreducible character 70.8
irreducible characters, computation 69.15
Irreducible Maximal Finite Integral Matrix Groups 48.12
Irreducible Solvable Matrix Groups 48.11
IrreducibleDifferences 70.10.3
IrreducibleModules 69.13.1
IrreducibleModules, for groups with pcgs 43.16
IrreducibleRepresentations 69.12.4
IrreducibleRepresentationsDixon 69.12.5
IrreducibleSolvableGroup 48.11.6
IrreducibleSolvableGroupMS 48.11.1
Is16BitsFamily 35.6.7
Is32BitsFamily 35.6.7
Is8BitsFamily 35.6.7
IsAbelian 33.4.9
IsAbelian, for character tables 69.8
IsAbelianNumberField 58.2.2
IsAbelianNumberFieldPolynomialRing 64.14.6
IsAbelianTom 68.8.1
IsAdditiveElement 30.14.3
IsAdditiveElementWithInverse 30.14.7
IsAdditiveElementWithZero 30.14.5
IsAdditiveGroup 53.1.6
IsAdditiveGroupGeneralMapping 31.9.4
IsAdditiveGroupHomomorphism 31.9.4
IsAdditivelyCommutative 53.3.1
IsAdditivelyCommutativeElement 30.15.2
IsAdditivelyCommutativeElementCollColl 30.15.2
IsAdditivelyCommutativeElementCollection 30.15.2
IsAdditivelyCommutativeElementFamily 30.15.2
IsAdditiveMagma 53.1.4
IsAdditiveMagmaWithInverses 53.1.6
IsAdditiveMagmaWithZero 53.1.5
IsAlgebra 60.7.3
IsAlgebraGeneralMapping 31.11.3
IsAlgebraHomomorphism 31.11.3
IsAlgebraicElement 65.2.1
IsAlgebraicExtension 65.1.2
IsAlgebraModuleElement 60.10.8
IsAlgebraModuleElementCollection 60.10.8
IsAlgebraModuleElementFamily 60.10.8
IsAlgebraWithOne 60.7.4
IsAlgebraWithOneGeneralMapping 31.11.4
IsAlgebraWithOneHomomorphism 31.11.4
IsAlphaChar 26.3.4
IsAlternatingGroup 41.3.4
IsAnticommutative 54.4.6
IsAntisymmetricBinaryRelation 32.2.4
IsAssociated 54.5.3
IsAssociative 33.4.7
IsAssociativeElement 30.15.1
IsAssociativeElementCollColl 30.15.1
IsAssociativeElementCollection 30.15.1
IsAssocWord 35.1.1
IsAssocWordWithInverse 35.1.1
IsAssocWordWithOne 35.1.1
IsAutomorphismGroup 38.7.4
IsBasicWreathLessThanOrEqual 35.3.4
IsBasicWreathProductOrdering 29.3.12
IsBasis 59.4.1
IsBasisByNiceBasis 59.10.5
IsBasisOfAlgebraModuleElementSpace 60.10.14
IsBergerCondition 72.1.3
IsBijective 31.2.6
IsBinaryRelation 32.1.1
IsBinaryRelation, same as IsEndoGeneralMapping 32.0
IsBLetterAssocWordRep 35.6.3
IsBLetterWordsFamily 35.6.4
IsBlist 22.0
IsBlockMatrixRep 24.15
IsBool 20.0
IsBound and Unbind for Lists 21.5
IsBound and Unbind for Records 27.5
IsBound, for lists 21.5.1
IsBoundGlobal 4.9.5
IsBrauerTable 69.4.1
IsBravaisGroup 42.5.10
IsBuiltFromAdditiveMagmaWithInverses 36.3.1
IsBuiltFromGroup 36.3.6
IsBuiltFromMagma 36.3.2
IsBuiltFromMagmaWithInverses 36.3.4
IsBuiltFromMagmaWithOne 36.3.3
IsBuiltFromSemigroup 36.3.5
IsCanonicalBasis 59.6.1
IsCanonicalBasisFullMatrixModule 59.8.10
IsCanonicalBasisFullRowModule 59.8.9
IsCanonicalNiceMonomorphism 38.5.4
IsCanonicalPcgs 43.8.1
IsCentral 33.4.8
IsCentralFactor 37.24.7
IsChar 26.0
IsCharacter 70.8.1
IsCharacteristicSubgroup 37.3.7
IsCharacterTable 69.4.1
IsCharacterTableInProgress 69.4.1
IsCharCollection 26.0
IsCheapConwayPolynomial 57.5.2
IsClassFunction 70.0
IsClassFusionOfNormalSubgroup 69.10.3
IsClosedStream 10.1.2
IsCochain 61.12.2
IsCochainCollection 61.12.2
IsCollection 28.0
IsCollectionFamily 28.1.2
IsCommutative 33.4.9
IsCommutativeElement 30.15.3
IsCommutativeElementCollColl 30.15.3
IsCommutativeElementCollection 30.15.3
IsCompositionMappingRep 31.1.6
IsConfluent 36.1.5
IsConfluent, for pc groups 44.4.7
IsConjugacyClassSubgroupsByStabilizerRep 37.19.2
IsConjugacyClassSubgroupsRep 37.19.2
IsConjugate 37.10.9
IsConjugatorAutomorphism 38.6.4
IsConjugatorIsomorphism 38.6.4
IsConstantRationalFunction 64.4.11
IsConstantTimeAccessGeneralMapping 31.12.2
IsConstantTimeAccessList 21.1.5
IsContainedInSpan 59.7.5
IsCopyable 12.6.1
IsCyc 18.1.3
IsCyclic 37.15.1
IsCyclic, for character tables 69.8
IsCyclicTom 68.8.1
IsCyclotomic 18.1.3
IsCyclotomicField 58.2.3
IsCyclotomicMatrixGroup 42.5.1
IsDenseList 21.1.2
IsDiagonalMat 24.3.8
IsDigitChar 26.3.1
IsDirectoryPath 9.6.5
IsDistributive 54.4.5
IsDivisionRing 56.1.1
IsDomain 30.9.1
IsDoneIterator 28.7.4
IsDoubleCoset 37.9.4
IsDuplicateFree 21.17.2
IsDuplicateFreeList 21.17.2
IsDxLargeGroup 69.15.8
IsElementaryAbelian 37.15.2
IsElementaryAbelian, for character tables 69.8
IsElementOfFpMonoid 51.0
IsElementOfFpSemigroup 51.0
IsElementOfFreeMagmaRing 63.2.1
IsElementOfFreeMagmaRingCollection 63.2.1
IsElementOfFreeMagmaRingFamily 63.2.2
IsElementOfMagmaRingModuloRelations 63.4.1
IsElementOfMagmaRingModuloRelationsCollection 63.4.1
IsElementOfMagmaRingModuloRelationsFamily 63.4.2
IsElementOfMagmaRingModuloSpanOfZeroFamily 63.5.1
IsEmpty 28.3.1
IsEmptyString 26.2.3
IsEndOfStream 10.3.7
IsEndoGeneralMapping 31.12.3
IsEndoGeneralMapping, same as IsBinaryRelation 32.0
IsEqualSet 21.19.2
IsEquivalenceClass 32.7.1
IsEquivalenceRelation 32.2.8
IsEuclideanRing 54.6.1
IsEvenInt 14.1.4
IsExecutableFile 9.6.4
IsExistingFile 9.6.1
IsExtAElement 30.14.1
IsExternalOrbit 39.11.8
IsExternalSet 39.11.1
IsExternalSubset 39.11.6
IsExtLElement 30.14.8
IsExtRElement 30.14.9
IsFamilyPcgs 44.1.2
IsFFE 57.1.1
IsFFECollColl 57.1.1
IsFFECollection 57.1.1
IsField 56.1.2
IsFieldControlledByGaloisGroup 56.3
IsFieldHomomorphism 31.11.5
IsFinite 28.3.2
IsFinite, for character tables 69.8
IsFiniteDimensional 55.3.5
IsFiniteDimensional, for matrix algebras 60.7.7
IsFiniteFieldPolynomialRing 64.14.5
IsFinitelyGeneratedGroup 37.15.12
IsFiniteOrderElement 30.15.4
IsFiniteOrderElementCollColl 30.15.4
IsFiniteOrderElementCollection 30.15.4
IsFiniteOrdersPcgs 43.4.2
IsFixedStabilizer 41.10.9
IsFLMLOR 60.7.1
IsFLMLORWithOne 60.7.2
IsFpGroup 45.0
IsFpMonoid 51.0
IsFpSemigroup 51.0
IsFreeGroup 35.2.2
IsFreeLeftModule 55.3.1
IsFreeMagmaRing 63.1.3
IsFreeMagmaRingWithOne 63.1.4
IsFromFpGroupGeneralMappingByImages 38.10.9
IsFromFpGroupHomomorphismByImages 38.10.9
IsFromFpGroupStdGensGeneralMappingByImages 38.10.10
IsFromFpGroupStdGensHomomorphismByImages 38.10.10
IsFullHomModule 59.9.7
IsFullMatrixModule 55.3.11
IsFullRowModule 55.3.9
IsFullSubgroupGLorSLRespectingBilinearForm 42.4.2
IsFullSubgroupGLorSLRespectingQuadraticForm 42.4.6
IsFullSubgroupGLorSLRespectingSesquilinearForm 42.4.4
IsFullTransformationSemigroup 49.1.4
IsFunction 5.4.1
IsGAPRandomSource 14.5.4
IsGaussianIntegers 58.5.2
IsGaussianRationals 58.1.3
IsGaussianSpace 59.8.3
IsGaussInt 18.1.12
IsGaussRat 18.1.13
IsGeneralizedDomain 30.9.1
IsGeneralizedRowVector 21.12.1
IsGeneralLinearGroup 42.3.1
IsGeneralMapping 31.12.1
IsGeneralMappingFamily 31.13.2
IsGeneratorsOfStruct 30.3.2
IsGL 42.3.1
IsGlobalRandomSource 14.5.4
IsGreensClass 49.5.3
IsGreensDClass 49.5.3
IsGreensDRelation 49.5.2
IsGreensHClass 49.5.3
IsGreensHRelation 49.5.2
IsGreensJClass 49.5.3
IsGreensJRelation 49.5.2
IsGreensLClass 49.5.3
IsGreensLessThanOrEqual 49.5.4
IsGreensLRelation 49.5.2
IsGreensRClass 49.5.3
IsGreensRelation 49.5.2
IsGreensRRelation 49.5.2
IsGroup 37.2.6
IsGroupGeneralMapping 31.8.4
IsGroupGeneralMappingByAsGroupGeneralMappingByImages 38.10.2
IsGroupGeneralMappingByImages 38.10.1
IsGroupGeneralMappingByPcgs 38.10.6
IsGroupHClass 49.5.11
IsGroupHomomorphism 31.8.4
IsGroupOfAutomorphisms 38.7.1
IsGroupRing 63.1.5
IsHandledByNiceBasis 55.3.13
IsHandledByNiceBasis, for vector spaces 59.10.6
IsHandledByNiceMonomorphism 38.5.1
IsHasseDiagram 32.2.7
IsHomogeneousList 21.1.3
IsIdempotent 30.10.7
IsIdenticalObj 12.5.1
IsIncomparableUnder 29.2.3
IsInducedFromNormalSubgroup 72.2.4
IsInducedPcgs 43.7.1
IsInducedPcgsWrtSpecialPcgs 43.13.7
IsInfBitsFamily 35.6.7
IsInfinity 18.2.1
IsInjective 31.2.4
IsInnerAutomorphism 38.6.4
IsInputOutputStream 10.8.1
IsInputStream 10.1.3
IsInputTextNone 10.1.5
IsInputTextStream 10.1.4
IsInt 14.1.1
IsIntegerMatrixGroup 42.5.3
IsIntegers 14.0
IsIntegralBasis 59.6.2
IsIntegralCyclotomic 18.1.4
IsIntegralRing 54.4.1
IsInternallyConsistent 12.8.3
IsInternallyConsistent, for character tables 69.10.1
IsInternallyConsistent, for tables of marks 68.9.1
IsIrreducibleCharacter 70.8.3
IsIrreducibleRingElement 54.5.6
IsIterator 28.7.3
IsJacobianElement 30.15.5
IsJacobianElementCollColl 30.15.5
IsJacobianElementCollection 30.15.5
IsJacobianRing 54.4.8
IsLaurentPolynomial 64.4.10
IsLaurentPolynomialDefaultRep 64.20.7
IsLDistributive 54.4.3
IsLeftAlgebraModuleElement 60.10.9
IsLeftAlgebraModuleElementCollection 60.10.9
IsLeftIdeal 54.2.3
IsLeftIdealInParent 54.2.3
IsLeftModule 55.1.2
IsLeftModuleGeneralMapping 31.10.2
IsLeftModuleHomomorphism 31.10.2
IsLeftOperatorAdditiveGroup 55.1.1
IsLeftSemigroupIdeal 49.2.3
IsLeftVectorSpace 59.0
IsLessThanOrEqualUnder 29.2.8
IsLessThanUnder 29.2.7
IsLetterAssocWordRep 35.6.1
IsLetterWordsFamily 35.6.2
IsLexicographicallyLess 21.20.8
IsLexOrderedFFE 57.1.3
IsLieAbelian 61.5.1
IsLieAlgebra 60.7.5
IsLieMatrix 24.1.3
IsLieNilpotent 61.5.2
IsLieObject 61.1.2
IsLieObjectCollection 61.1.2
IsLieSolvable 61.5.3
IsLinearMapping 31.10.3
IsLinearMappingsModule 59.9.9
IsList 21.1.1
IsListDefault 21.12.3
IsListOrCollection 28.2.1
IsLogOrderedFFE 57.1.3
IsLowerAlphaChar 26.3.2
IsLowerTriangularMat 24.3.10
IsMagma 33.1.1
IsMagmaHomomorphism 31.7.1
IsMagmaRingModuloRelations 63.4.4
IsMagmaRingModuloSpanOfZero 63.5.2
IsMagmaWithInverses 33.1.4
IsMagmaWithInversesIfNonzero 33.1.3
IsMagmaWithOne 33.1.2
IsMapping 31.2.3
IsMatchingSublist 21.17.1
IsMatrix 24.1.1
IsMatrixGroup 42.0
IsMatrixModule 55.3.8
IsMatrixSpace 59.8.2
IsMersenneTwister 14.5.4
IsMinimalNonmonomial 72.4.1
IsModuloPcgs 43.9.2
IsMonoid 50.0
IsMonomial, for character tables 69.8
IsMonomial, for characters 72.3
IsMonomial, for groups 72.3
IsMonomial, for positive integers 72.3
IsMonomialGroup 37.15.9
IsMonomialMatrix 24.3.7
IsMonomialNumber 72.3.3
IsMonomialOrdering 64.16.1
IsMultiplicativeElement 30.14.10
IsMultiplicativeElementWithInverse 30.14.13
IsMultiplicativeElementWithOne 30.14.11
IsMultiplicativeElementWithZero 30.14.12
IsMultiplicativeGeneralizedRowVector 21.12.2
IsMultiplicativeZero 33.4.12
IsMutable 12.6.2
IsMutableBasis 59.7.1
IsNaturalAlternatingGroup 41.3.2
IsNaturalGL 42.3.2
IsNaturalGLnZ 42.5.4
IsNaturalSL 42.3.4
IsNaturalSLnZ 42.5.5
IsNaturalSymmetricGroup 41.3.1
IsNearAdditiveElement 30.14.2
IsNearAdditiveElementWithInverse 30.14.6
IsNearAdditiveElementWithZero 30.14.4
IsNearAdditiveGroup 53.1.3
IsNearAdditiveMagma 53.1.1
IsNearAdditiveMagmaWithInverses 53.1.3
IsNearAdditiveMagmaWithZero 53.1.2
IsNearlyCharacterTable 69.4.1
IsNearRingElement 30.14.15
IsNearRingElementWithInverse 30.14.19
IsNearRingElementWithOne 30.14.17
IsNegRat 16.1.3
IsNilpotent, for character tables 69.8
IsNilpotent, for groups with pcgs 43.16
IsNilpotentElement 61.9.5
IsNilpotentGroup 37.15.3
IsNilpotentTom 68.8.1
IsNonassocWord 34.1.3
IsNonassocWordCollection 34.1.4
IsNonassocWordWithOne 34.1.3
IsNonassocWordWithOneCollection 34.1.4
IsNonnegativeIntegers 14.0
IsNonSPGeneralMapping 31.13.1
IsNonTrivial 28.3.4
IsNormal 37.3.6
IsNormalBasis 59.6.3
IsNotIdenticalObj 12.5.2
IsNumberField 58.2.1
IsObject 12.1.1
IsOddInt 14.1.5
isomorphic, pc group 44.4 44.5
IsomorphicSubgroups 38.9.3
IsomorphismFpAlgebra 60.9.9
IsomorphismFpGroup 45.10.1
IsomorphismFpGroup, for subgroups of fp groups 45.11
IsomorphismFpGroupByGenerators 45.10.2
IsomorphismFpGroupByGeneratorsNC 45.10.2
IsomorphismFpGroupByPcgs 44.3.2
IsomorphismFpSemigroup 51.1.3
IsomorphismGroups 38.9.1
IsomorphismMatrixAlgebra 60.9.10
IsomorphismPcGroup 44.5.2
IsomorphismPermGroup 41.2.1
IsomorphismPermGroup, for Imf matrix groups 48.12.5
IsomorphismPermGroupImfGroup 48.12.6
IsomorphismReesMatrixSemigroup 49.6.11
IsomorphismRefinedPcGroup 44.4.8
IsomorphismRepStruct 30.5.1
isomorphisms, find all 38.9
IsomorphismSCAlgebra 60.9.11
IsomorphismSimplifiedFpGroup 45.11.1
IsomorphismSpecialPcGroup 44.5.3
IsomorphismTransformationSemigroup 49.1.3
IsomorphismTypeInfoFiniteSimpleGroup 37.15.11
IsOne 30.10.5
IsOperation 5.4.2
IsOrdering 29.0
IsOrderingOnFamilyOfAssocWords 29.3.1
IsOrdinaryMatrix 24.1.2
IsOrdinaryTable 69.4.1
IsOutputStream 10.1.6
IsOutputTextNone 10.1.8
IsOutputTextStream 10.1.7
IsPadicExtensionNumber 66.2.3
IsPadicExtensionNumberFamily 66.2.4
IsParentPcgsFamilyPcgs 44.1.4
IsPartialOrderBinaryRelation 32.2.6
IsPcGroup 44.3.1
IsPcGroupGeneralMappingByImages 38.10.7
IsPcGroupHomomorphismByImages 38.10.7
IsPcgs 43.2.2
IsPcgsCentralSeries 43.11.5
IsPcgsChiefSeries 43.11.13
IsPcgsElementaryAbelianSeries 43.11.1
IsPcgsPCentralSeriesPGroup 43.11.9
IsPerfect, for character tables 69.8
IsPerfectGroup 37.15.5
IsPerfectTom 68.8.1
IsPerm 40.0
IsPermCollColl 40.0
IsPermCollection 40.0
IsPermGroup 41.0
IsPermGroupGeneralMappingByImages 38.10.4
IsPermGroupHomomorphismByImages 38.10.4
IsPGroup 37.15.14
IsPNilpotent 37.15.19
IsPolycyclicGroup 37.15.7
IsPolynomial 64.4.4
IsPolynomialDefaultRep 64.20.5
IsPolynomialFunction 64.4.1
IsPolynomialFunctionsFamily 64.18.2
IsPolynomialRing 64.14.4
IsPosInt 14.1.2
IsPositiveIntegers 14.0
IsPosRat 16.1.2
IsPreimagesByAsGroupGeneralMappingByImages 38.10.3
IsPreOrderBinaryRelation 32.2.5
IsPrime 54.5.7
IsPrimeField 56.2.5
IsPrimeInt 14.3.2
IsPrimeOrdersPcgs 43.4.3
IsPrimePowerInt 14.3.3
IsPrimitive 39.9.7
IsPrimitiveCharacter 72.2.2
IsPrimitivePolynomial 64.4.12
IsPrimitiveRootMod 15.2.4
IsProbablyPrimeInt 14.3.2
IsPseudoCanonicalBasisFullHomModule 59.9.8
IsPSolvable 37.15.18
IsPSolvableCharacterTable 69.10.2
IsPSolvableCharacterTableOp 69.10.2
IsPurePadicNumber 66.1.5
IsPurePadicNumberFamily 66.1.6
IsQuasiPrimitive 72.2.3
IsQuaternion 60.7.8
IsQuaternionCollColl 60.7.8
IsQuaternionCollection 60.7.8
IsQuickPositionList 21.23.1
IsQuotientSemigroup 49.4.1
IsRandomSource 14.5.1
IsRange 21.22.1
IsRat 16.1.1
IsRationalFunction 64.4.1
IsRationalFunctionDefaultRep 64.20.1
IsRationalFunctionsFamily 64.18.2
IsRationalMatrixGroup 42.5.2
IsRationals 16.0
IsRationalsPolynomialRing 64.14.7
IsRDistributive 54.4.4
IsReadableFile 9.6.2
IsReadOnlyGlobal 4.9.1
IsRecord 27.0
IsRecordCollColl 27.0
IsRecordCollection 27.0
IsReduced 36.1.7
IsReductionOrdering 29.3.3
IsReesCongruence 49.3.2
IsReesCongruenceSemigroup 49.0
IsReesMatrixSemigroup 49.6.3
IsReesMatrixSemigroupElement 49.6.6
IsReesZeroMatrixSemigroup 49.6.4
IsReesZeroMatrixSemigroupElement 49.6.6
IsReflexiveBinaryRelation 32.2.1
IsRegular 39.9.5
IsRegularDClass 49.5.12
IsRegularSemigroup 49.0
IsRegularSemigroupElement 49.0
IsRelativelySM 72.3.6
IsRestrictedLieAlgebra 61.8.1
IsRewritingSystem 36.1.1
IsRightAlgebraModuleElement 60.10.10
IsRightAlgebraModuleElementCollection 60.10.10
IsRightCoset 37.7.4
IsRightIdeal 54.2.3
IsRightIdealInParent 54.2.3
IsRightModule 55.1.7
IsRightOperatorAdditiveGroup 55.1.6
IsRightSemigroupIdeal 49.2.3
IsRing 54.1.1
IsRingElement 30.14.16
IsRingElementWithInverse 30.14.20
IsRingElementWithOne 30.14.18
IsRingGeneralMapping 31.11.1
IsRingHomomorphism 31.11.1
IsRingWithOne 54.3.1
IsRingWithOneGeneralMapping 31.11.2
IsRingWithOneHomomorphism 31.11.2
IsRootSystem 61.7.3
IsRootSystemFromLieAlgebra 61.7.4
IsRowModule 55.3.7
IsRowSpace 59.8.1
IsRowVector 23.0
IsScalar 30.14.20
IsSemiEchelonized 59.8.7
IsSemigroup 49.0
IsSemigroupCongruence 49.3.1
IsSemigroupIdeal 49.2.3
IsSemiRegular 39.9.4
IsSet 21.17.4
IsShortLexLessThanOrEqual 35.3.3
IsShortLexOrdering 29.3.7
IsSimple, for character tables 69.8
IsSimpleAlgebra 60.7.6
IsSimpleGroup 37.15.10
IsSimpleSemigroup 49.0
IsSingleValued 31.2.2
IsSL 42.3.3
IsSolvable, for character tables 69.8
IsSolvableGroup 37.15.6
IsSolvableTom 68.8.1
IsSortedList 21.17.3
IsSpecialLinearGroup 42.3.3
IsSpecialPcgs 43.13.1
IsSPGeneralMapping 31.13.1
IsSporadicSimple, for character tables 69.8
IsSSortedList 21.17.4
IsStandardGeneratorsOfGroup 68.10.4
IsStraightLineProgElm 35.9.1
IsStraightLineProgram 35.8.1
IsStream 10.1.1
IsString 26.0
IsStringRep 26.2.1
IsStruct 30.6.1
IsSubgroup 37.3.5
IsSubgroupFpGroup 45.0
IsSubgroupOfWholeGroupByQuotientRep 45.12.2
IsSubgroupSL 42.3.5
IsSubmonoidFpMonoid 51.0
IsSubnormal 37.3.10
IsSubnormallyMonomial 72.3.5
IsSubsemigroupFpSemigroup 51.0
IsSubset 28.4.1
IsSubsetBlist 22.1.4
IsSubsetLocallyFiniteGroup 37.15.13
IsSubsetSet 21.19.3
IsSubspacesVectorSpace 59.3.2
IsSubstruct 30.8.4
IsSupersolvable, for character tables 69.8
IsSupersolvable, for groups with pcgs 43.16
IsSupersolvableGroup 37.15.8
IsSurjective 31.2.5
IsSyllableAssocWordRep 35.6.5
IsSyllableWordsFamily 35.6.6
IsSymmetricBinaryRelation 32.2.2
IsSymmetricGroup 41.3.3
IsTable 21.1.4
IsTableOfMarks 68.6.2
IsTableOfMarksWithGens 68.11.3
IsToPcGroupGeneralMappingByImages 38.10.8
IsToPcGroupHomomorphismByImages 38.10.8
IsToPermGroupGeneralMappingByImages 38.10.5
IsToPermGroupHomomorphismByImages 38.10.5
IsTotal 31.2.1
IsTotalOrdering 29.2.2
IsTransformation 52.0
IsTransformationCollection 52.0
IsTransformationMonoid 49.1.1
IsTransformationSemigroup 49.1.1
IsTransitive, for characters 70.8.15
IsTransitive, for class functions 70.8
IsTransitive, for group actions 39.9.1
IsTransitiveBinaryRelation 32.2.3
IsTranslationInvariantOrdering 29.3.2
IsTrivial 28.3.3
IsTuple 31.0
IsTwoSidedIdeal 54.2.3
IsTwoSidedIdealInParent 54.2.3
IsUEALatticeElement 61.13.5
IsUEALatticeElementCollection 61.13.5
IsUEALatticeElementFamily 61.13.5
IsUniqueFactorizationRing 54.4.2
IsUnit 54.5.1
IsUnivariatePolynomial 64.4.8
IsUnivariatePolynomialRing 64.15.2
IsUnivariateRationalFunction 64.4.6
IsUnknown 19.0
IsUpperAlphaChar 26.3.3
IsUpperTriangularMat 24.3.9
IsValidIdentifier 4.6.1
IsVector 30.14.14
IsVectorSpace 59.0
IsVirtualCharacter 70.8.2
IsWeightLexOrdering 29.3.9
IsWeightRepElement 61.13.8
IsWeightRepElementCollection 61.13.8
IsWeightRepElementFamily 61.13.8
IsWellFoundedOrdering 29.2.1
IsWeylGroup 61.7.15
IsWholeFamily 28.3.5
IsWLetterAssocWordRep 35.6.3
IsWLetterWordsFamily 35.6.4
IsWord 34.1.1
IsWordCollection 34.1.2
IsWordWithInverse 34.1.1
IsWordWithOne 34.1.1
IsWreathProductOrdering 29.3.14
IsWritableFile 9.6.3
IsZero 30.10.6
IsZeroGroup 49.0
IsZeroSimpleSemigroup 49.0
IsZeroSquaredElement 30.15.6
IsZeroSquaredElementCollColl 30.15.6
IsZeroSquaredElementCollection 30.15.6
IsZeroSquaredRing 54.4.7
IsZmodnZObj 14.4.4
IsZmodnZObjNonprime 14.4.4
IsZmodpZObj 14.4.4
IsZmodpZObjLarge 14.4.4
IsZmodpZObjSmall 14.4.4
Iterated 21.20.25
Iterator 28.7.1
iterator, for low index subgroups 45.9
IteratorByBasis 59.5.6
IteratorByFunctions 28.7.8
IteratorList 28.7.6
Iterators 28.7
IteratorSorted 28.7.2

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GAP 4 manual
December 2008