- Introduction
- Creation of a Permutation Group
- Elementary Properties of a Group
- Homomorphisms
- Building Permutation Groups
- Some Standard Permutation Groups
- AbelianGroup(GrpPerm, Q) : Cat, [ RngIntElt ] -> GrpPerm
- AlternatingGroup(GrpPerm, n) : Cat, RngIntElt -> GrpPerm
- CyclicGroup(GrpPerm, n) : Cat, RngIntElt -> GrpPerm
- DihedralGroup(GrpPerm, n) : Cat, RngIntElt -> GrpPerm
- Sym(GrpPerm, n) : Cat, RngIntElt -> GrpPerm
- ExtraSpecialGroup(GrpPerm, p, n : parameters) : Cat, RngIntElt, RngIntElt -> GrpPerm
- YoungSubgroup(L) : [RngIntElt] -> GrpPerm
- Example GrpPerm_StandardGroups (H64E7)
- Direct Products and Wreath Products
- DirectProduct(G, H) : GrpPerm, GrpPerm -> GrpPerm, [ Hom(Grp) ], [ Hom(Grp) ]
- DirectProduct(Q) : [ GrpPerm ] -> GrpPerm, [ Hom(Grp) ], [ Hom(Grp) ]
- PrimitiveWreathProduct(G, H) : GrpPerm, GrpPerm -> GrpPerm
- PrimitiveWreathProduct(Q) : [ GrpPerm ] -> GrpPerm
- WreathProduct(G, H) : GrpPerm, GrpPerm -> GrpPerm, SeqEnum[Map], Map, Map
- WreathProduct(Q) : [ GrpPerm ] -> GrpPerm
- WreathProduct(B) : GSet -> GrpPerm, GrpPerm, GrpPerm
- WreathProduct(G, B) : GrpPerm, GSet -> GrpPerm, GrpPerm, GrpPerm
- Example GrpPerm_Products (H64E8)
- Permutations
- Coercion
- Arithmetic with Permutations
- g * h : GrpPermElt, GrpPermElt -> GrpPermElt
- g ^ n : GrpPermElt, RngIntElt -> GrpPermElt
- g / h : GrpPermElt, GrpPermElt -> GrpPermElt
- g ^ h : GrpPermElt, GrpPermElt -> GrpPermElt
- (g, h) : GrpPermElt, GrpPermElt -> GrpPermElt
- (g1, ..., gr) : GrpPermElt, ..., GrpPermElt -> GrpPermElt
- Properties of Permutations
- Predicates for Permutations
- Set Operations
- Conjugacy
- Class(H, x) : GrpPerm, GrpPermElt -> { GrpPermElt }
- ConjugacyClasses(G: parameters) : GrpPerm -> [ <RngIntElt, RngIntElt, GrpPermElt> ]
- ClassRepresentative(G, x) : GrpPerm, GrpPermElt -> GrpPermElt
- ClassCentraliser(G, i) : GrpPerm, RngIntElt -> GrpPerm
- ClassMap(G: parameters) : GrpPerm -> Map
- IsConjugate(G, g, h: parameters) : GrpPerm, GrpPermElt, GrpPermElt -> BoolElt, GrpPermElt
- IsConjugate(G, H, K: parameters) : GrpPerm, GrpPerm, GrpPerm -> BoolElt, GrpPermElt
- Exponent(G) : GrpPerm -> RngIntElt
- NumberOfClasses(G) : GrpPerm -> RngIntElt
- PowerMap(G) : GrpPerm -> Map
- AssertAttribute(G, "Classes", Q) : GrpPerm, MonStgElt, SeqEnum ->
- Example GrpPerm_Classes (H64E12)
- Example GrpPerm_Classes-2 (H64E13)
- Subgroups
- Construction of a Subgroup
- Membership and Equality
- Elementary Properties of a Subgroup
- Index(G, H) : GrpPerm, GrpPerm -> RngIntElt
- FactoredIndex(G, H) : GrpPerm, GrpPerm -> [ <RngIntElt, RngIntElt> ]
- IsCentral(G, H) : GrpPerm, GrpPerm -> BoolElt
- IsNormal(G, H) : GrpPerm, GrpPerm -> BoolElt
- IsSelfNormalizing(G, H) : GrpPerm, GrpPerm -> BoolElt
- IsSubnormal(G, H) : GrpPerm, GrpPerm -> BoolElt
- Standard Subgroups
- H ^ g : GrpPerm, GrpPermElt -> GrpPerm
- H meet K : GrpPerm, GrpPerm -> GrpPerm
- IntersectionWithNormalSubgroup(G, N: parameters) : GrpPerm, GrpPerm -> GrpPerm
- CommutatorSubgroup(G, H, K) : GrpPerm, GrpPerm, GrpPerm -> GrpPerm
- Centralizer(G, g: parameters) : GrpPerm, GrpPermElt -> GrpPerm
- Centralizer(G, H) : GrpPerm, GrpPerm -> GrpPerm
- CentralizerOfNormalSubgroup(G, H) : GrpPerm, GrpPerm -> GrpPerm
- SectionCentraliser(G, H, K) : GrpPerm, GrpPerm, GrpPerm -> GrpPerm
- Core(G, H) : GrpPerm, GrpPerm -> GrpPerm
- H ^ G : GrpPerm, GrpPerm -> GrpPerm
- Normalizer(G, H: parameters) : GrpPerm, GrpPerm -> GrpPerm
- SymmetricNormalizer(G) : GrpPerm -> GrpPerm
- SylowSubgroup(G, p) : GrpPerm, RngIntElt -> GrpPerm
- Example GrpPerm_SubgroupConstructions (H64E17)
- Maximal Subgroups
- IsMaximal(G, H: parameters) : GrpPerm, GrpPerm -> BoolElt
- IsProbablyMaximal(G, H: parameters) : GrpPerm, GrpPerm -> BoolElt
- MaximalSubgroups(G: parameters) : GrpPerm -> [ rec< GrpPerm, RngIntElt, RngIntElt, GrpFP> ]
- Example GrpPerm_Maximals (H64E18)
- MaximalSubgroups(G,N: parameters) : GrpPerm, GrpPerm -> [ rec< GrpPerm, RngIntElt, RngIntElt, GrpFP> ]
- Conjugacy Classes of Subgroups
- SubgroupClasses(G: parameters) : GrpPerm -> [ rec< GrpPerm, RngIntElt, RngIntElt, GrpFP> ]
- SubgroupsLift(G, A, B, Q: parameters) : GrpPerm, GrpPerm, GrpPerm, SeqEnum -> SeqEnum
- LowIndexSubgroups(G, n: parameters) : GrpPerm, RngIntElt -> SeqEnum
- LowIndexSubgroups(G, N, n: parameters) : GrpPerm, RngIntElt -> SeqEnum
- Example GrpPerm_Subgroups (H64E19)
- Example GrpPerm_low-index-subs (H64E20)
- Example GrpPerm_Subgroups-2 (H64E21)
- SubgroupLattice(G) : GrpPerm -> SubGrpLat
- BurnsideMatrix(G) : GrpPerm -> AlgMatElt
- DisplayBurnsideMatrix(G) : GrpPerm ->
- TableOfMarks(G) : GrpPerm -> AlgMatElt
- Classes of Subgroups Satisfying a Condition
- NormalSubgroups(G: parameters) : GrpPerm -> [ rec< GrpPerm, RngIntElt, RngIntElt, GrpFP> ]
- ElementaryAbelianSubgroups(G: parameters) : GrpPerm -> [ rec< GrpPerm, RngIntElt, RngIntElt, GrpFP> ]
- CyclicSubgroups(G: parameters) : GrpPerm -> [ rec< GrpPerm, RngIntElt, RngIntElt, GrpFP> ]
- AbelianSubgroups(G: parameters) : GrpPerm -> [ rec< GrpPerm, RngIntElt, RngIntElt, GrpFP> ]
- NilpotentSubgroups(G: parameters) : GrpPerm -> [ rec< GrpPerm, RngIntElt, RngIntElt, GrpFP> ]
- SolvableSubgroups(G: parameters) : GrpPerm -> [ rec< GrpPerm, RngIntElt, RngIntElt, GrpFP> ]
- PerfectSubgroups(G: parameters) : GrpPerm -> [ rec< GrpPerm, RngIntElt, RngIntElt, GrpFP> ]
- NonsolvableSubgroups(G: parameters) : GrpPerm -> [ rec< GrpPerm, RngIntElt, RngIntElt, GrpFP> ]
- SimpleSubgroups(G: parameters) : GrpPerm -> [ rec< GrpPerm, RngIntElt, RngIntElt, GrpFP> ]
- Quotient Groups
- Construction of Quotient Groups
- Abelian, Nilpotent and Soluble Quotients
- AbelianQuotient(G) : GrpPerm -> GrpAb, Map
- ElementaryAbelianQuotient(G, p) : GrpPerm, RngIntElt -> GrpAb, Map
- pQuotient(G, p, c) : GrpPerm, RngIntElt, RngIntElt -> GrpPC, Map, SeqEnum, BoolElt
- NilpotentQuotient(G, c) : GrpPerm, RngIntElt -> GrpGPC, Map
- SolvableQuotient(G): GrpPerm -> GrpPC, Map, SeqEnum, MonStgElt
- Example GrpPerm_SpecialQuotient (H64E23)
- Permutation Group Actions
- G-Sets
- Creating a G-Set
- GSetFromIndexed(G, Y) : GrpPerm, SetIndx -> GSet
- GSet(G, X, Y) : GrpPerm, GSet, SetEnum -> GSet
- GSet(G) : GrpPerm -> GSet
- GSet(G, Y, f) : GrpPerm, Set, Map -> GSet
- Action(Y) : GSet -> Map
- Group(Y) : GSet -> GrpPerm
- Labelling(G) : GrpPerm -> SetIndx
- Degree(g, Y) : GrpPermElt, GSet -> RngIntElt
- Degree(G, Y) : GrpPerm, GSet -> RngIntElt
- Support(g, Y) : GrpPermElt, GSet -> { Elt }
- Support(G, Y) : GrpPerm, GSet -> { Elt }
- Example GrpPerm_GSets (H64E24)
- Images, Orbits and Stabilizers
- x ^ g : Elt, GrpPermElt -> Elt
- Image(g, Y, y) : GrpPermElt, GSet, Elt -> Elt
- Fix(g, Y): GrpPermElt, GSet -> { Elt }
- Fix(G, Y) : GrpPerm, GSet -> { Elt }
- x ^ G : Elt, GrpPerm -> GSet
- Cycle(e, x) : GrpPermElt, Elt -> SetIndx
- CycleDecomposition(e) : GrpPermElt -> SeqEnum[SetIndx]
- Orbit(G, Y, y) : GrpPerm, GSet, Elt -> GSet
- Orbits(G, Y) : GrpPerm, GSet -> [ GSet ]
- OrbitRepresentatives(G) : GrpPerm -> SeqEnum
- OrbitClosure(G, Y, S) : GrpPerm, GSet, { Elt } -> GSet
- IsConjugate(G, Y, y, z) : GrpPerm, GSet, Elt, Elt -> BoolElt, GrpPermElt
- Stabilizer(G, Y, y) : GrpPerm, GSet, Elt -> GrpPerm
- IsPrimitive(G, Y) : GrpPerm, GSet -> BoolElt
- IsTransitive(G, Y) : GrpPerm, GSet -> BoolElt
- IsTransitive(G, Y, k) : GrpPerm, GSet, RngIntElt -> BoolElt
- IsSharplyTransitive(G, Y, k) : GrpPerm, GSet, RngIntElt -> BoolElt
- Transitivity(G, Y) : GrpPerm, GSet -> RngIntElt
- IsRegular(G, Y) : GrpPerm, GSet -> BoolElt
- IsSemiregular(G, Y) : GrpPerm, GSet -> BoolElt
- IsSemiregular(G, Y, S) : GrpPerm, GSet, SetEnum -> BoolElt
- IsFrobenius(G) : GrpPerm -> BoolElt
- Example GrpPerm_Stabilizers (H64E25)
- Action on a G-Space
- Action(G, Y) : GrpPerm, GSet -> Hom(Grp), GrpPerm, GrpPerm
- ActionImage(G, Y) : GrpPerm, GSet -> GrpPerm
- ActionKernel(G, Y) : GrpPerm, GSet -> GrpPerm
- IsFaithful(G, Y) : GrpPerm, GSet -> BoolElt
- Example GrpPerm_Actions (H64E26)
- Action on Orbits
- OrbitAction(G, T) : GrpPerm, GSet -> Hom(Grp), GrpPerm, GrpPerm
- OrbitImage(G, T) : GrpPerm, GSet -> GrpPerm
- OrbitKernel(G, T) : GrpPerm, GSet -> GrpPerm
- IsOrbit(G, S) : GrpPerm, { Elt } -> BoolElt
- Example GrpPerm_OrbitActions (H64E27)
- Action on a G-invariant Partition
- IsBlock(G, S) : GrpPerm, { Elt } -> BoolElt
- IsPrimitive(G) : GrpPerm -> BoolElt
- MaximalPartition(G) : GrpPerm -> GSet
- MinimalPartition(G: parameters) : GrpPerm -> GSet
- MinimalPartitions(G: parameters) : GrpPerm -> [ GSet ]
- MinimalBlocks(G: parameters) : GrpPerm -> [ SetEnum ]
- AllPartitions(G) : GrpPerm -> SetEnum
- BlocksAction(G, P) : GrpPerm, Any -> Hom(GrpPerm), GrpPerm, GrpPerm
- BlocksImage(G, P) : GrpPerm, Any -> GrpPerm
- BlocksKernel(G, P) : GrpPerm, Any -> GrpPerm
- Example GrpPerm_BlocksActions (H64E28)
- Example GrpPerm_BlocksActions-2 (H64E29)
- Action on a Coset Space
- Reduced Permutation Actions
- The Jellyfish Algorithm
- Normal and Subnormal Subgroups
- Characteristic Subgroups and Normal Series
- DerivedSeries(G) : GrpPerm -> [ GrpPerm ]
- CompositionSeries(G) : GrpPerm -> [ GrpPerm ]
- CommutatorSubgroup(G) : GrpPerm -> GrpPerm
- SolubleResidual(G) : GrpPerm -> GrpPerm
- DerivedLength(G) : GrpPerm -> RngIntElt
- LowerCentralSeries(G) : GrpPerm -> [ GrpPerm ]
- NilpotencyClass(G) : GrpPerm -> RngIntElt
- UpperCentralSeries(G) : GrpPerm -> [ GrpPerm ]
- Centre(G) : GrpPerm -> GrpPerm
- Hypercentre(G) : GrpPerm -> GrpPerm
- pCore(G, p) : GrpPerm, RngIntElt -> GrpPerm
- pCoreQuotient(G, p) : GrpPerm, RngIntElt -> GrpPerm, Map, GrpPerm
- FittingGroup(G) : GrpPerm -> GrpPerm
- FrattiniSubgroup(G) : GrpPerm -> GrpPerm
- JenningsSeries(G) : GrpPerm -> [ GrpPerm ]
- pCentralSeries(G, p) : GrpPerm, RngIntElt -> [ GrpPerm ]
- SubnormalSeries(G, H) : GrpPerm, GrpPerm -> [ GrpPerm ]
- Example GrpPerm_Series (H64E30)
- Maximal and Minimal Normal Subgroups
- Lattice of Normal Subgroups
- Composition and Chief Series
- ChiefFactors(G) : GrpPerm -> [ <RngIntElt, RngIntElt, RngIntElt, RngIntElt> ]
- ChiefSeries(G) : GrpPerm -> [ GrpPerm ], [ <RngIntElt, RngIntElt, RngIntElt, RngIntElt> ]
- CompositionFactors(G) : GrpPerm -> [ <RngIntElt, RngIntElt, RngIntElt> ]
- Example GrpPerm_CompFactors (H64E32)
- PrimaryAbelianInvariants(G) : GrpPerm -> [ RngIntElt ]
- PrimaryAbelianBasis(G) : GrpPerm -> [ GrpPermElt ], [ RngIntElt ]
- The Socle
- Socle(G) : GrpPerm -> GrpPerm
- SocleFactor(G) : GrpPerm -> GrpPerm
- SocleFactors(G) : GrpPerm -> [ GrpPerm ]
- SocleSeries(G) : GrpPerm -> [ GrpPerm ]
- EARNS(G) : GrpPerm -> GrpPerm
- AffineGeneralLinearGroup(E) : GrpPerm -> GrpPerm
- IsAffine(G) : GrpPerm -> BoolElt, GrpPerm
- AffineAction(G) : GrpPerm -> Hom, GrpPerm, GrpPerm
- AffineImage(G) : GrpPerm -> GrpPerm
- AffineKernel(G) : GrpPerm -> GrpPerm
- SocleAction(G) : GrpPerm -> Hom, GrpPerm, GrpPerm
- SocleImage(G) : GrpPerm -> GrpPerm
- SocleKernel(G) : GrpPerm -> GrpPerm
- SocleQuotient(G) : GrpPerm -> GrpPerm, Hom, GrpPerm
- RefineSection(G, M, N) : GrpPerm, GrpPerm, GrpPerm -> [ GrpPerm ]
- Example GrpPerm_PrimitiveStructure (H64E33)
- The Soluble Radical and its Quotient
- Complements and Supplements
- Complements(G, M) : GrpPerm, GrpPerm -> [ GrpPerm ]
- Complements(G, M, N) : GrpPerm, GrpPerm, GrpPerm -> [ GrpPerm ]
- HasComplement(G, M) : GrpPerm, GrpPerm -> BoolElt, GrpPerm
- Supplements(G, M) : GrpPerm, GrpPerm -> [ GrpPerm ]
- Supplements(G, M, N) : GrpPerm, GrpPerm, GrpPerm -> [ GrpPerm ]
- HasSupplement(G, M) : GrpPerm, GrpPerm -> BoolElt, GrpPerm
- Example GrpPerm_Complements (H64E35)
- Abelian Normal Subgroups
- AbelianNormalSubgroup(G) : GrpPerm -> GrpPerm
- AbelianNormalQuotient(G, H) : GrpPerm, GrpPerm -> GrpPerm, Hom(GrpPerm), GrpPerm
- SolubleNormalQuotient(G, H) : GrpPerm -> GrpPerm, Hom(GrpPerm), GrpPerm
- ElementaryAbelianNormalSubgroup(G) : GrpPerm -> GrpPerm
- pElementaryAbelianNormalSubgroup(G, p) : GrpPerm, RngIntElt -> GrpPerm
- MEANS(G) : GrpPerm -> GrpPerm
- MEANS(G, N) : GrpPerm, GrpPerm -> GrpPerm
- Cosets and Transversals
- Cosets
- H * g : GrpPerm, GrpPermElt -> Elt
- DoubleCoset(G, H, g, K) : GrpPerm, GrpPerm, GrpPermElt, GrpPerm -> GrpPermDcosElt
- DoubleCosetRepresentatives(G, H, K) : GrpPerm, GrpPerm, GrpPerm -> SeqEnum, SeqEnum
- DoubleCosetCanonical(G, H, g, K: parameters) : GrpPerm, GrpPerm, GrpPermElt, GrpPerm -> SeqEnum, SeqEnum
- ProcessLadder(L, G, U) : [GrpPerm], GrpPerm, GrpPerm -> Rec
- GetRep(p, R) : GrpPermElt, Rec -> GrpPermElt
- DeleteData(R) : Rec ->
- YoungSubgroupLadder(L) : [RngIntElt] -> [GrpPerm]
- StabilizerLadder(G, d) : GrpPerm, RngMPolElt -> [GrpPerm]
- x in C : GrpPermElt, Elt -> BoolElt
- x notin C : GrpPermElt, Elt -> BoolElt
- C1 eq C2 : Elt, Elt -> BoolElt
- C1 ne C2 : Elt, Elt -> BoolElt
- # C : Elt -> RngIntElt
- CosetTable(G, H) : Grp, Grp -> Map
- [Future release] CosetTable(G, f) : Grp, Map -> Map
- Transversals
- Presentations
- Automorphism Groups
- Cohomology
- pMultiplicator(G, p) : GrpPerm, RngIntElt -> [ RngIntElt ]
- pCover(G, F, p) : GrpPerm, GrpFP, RngIntElt -> GrpFP
- CohomologicalDimension(G, M, i) : GrpPerm, ModRng, RngIntElt -> RngIntElt
- ExtensionProcess(G, M, F) : GrpPerm, ModRng, GrpFP -> Process
- Extension(P, Q) : Process -> GrpFP
- SplitExtension(G, M, F) : GrpPerm, ModRng, GrpFP -> GrpFP
- Example GrpPerm_Cohomology (H64E37)
- Example GrpPerm_Cohomology-2 (H64E38)
- Representation Theory
- CharacterTable(G: parameters) : GrpPerm -> TabChtr
- PermutationCharacter(G) : GrpPerm -> AlgChtrElt
- PermutationCharacter(G, H) : GrpPerm, GrpPerm -> AlgChtrElt
- GModule(G, S) : Grp, AlgMat -> ModGrp
- GModule(G, A, B) : Grp, Grp, Grp -> ModGrp, Map
- PermutationModule(G, H, R) : Grp, Grp, Rng -> ModGrp
- PermutationModule(G, R) : GrpPerm, Rng -> ModGrp
- Example GrpPerm_GModule (H64E39)
- Identification
- Identification as an Abstract Group
- Identification as a Permutation Group
- IsAlternating(G) : GrpPerm -> BoolElt
- IsSymmetric(G) : GrpPerm -> BoolElt
- IsAltsym(G : parameters) : GrpPerm -> BoolElt
- TwoTransitiveGroupIdentification(G) : GrpPerm -> Tup
- IsEven(G): GrpPerm -> BoolElt
- RecogniseAlternatingOrSymmetric(G : parameters) : Grp, RngIntElt -> BoolElt, Map, Map, Map, Map, BoolElt
- AlternatingOrSymmetricElementToWord(G, g): Grp, GrpElt -> BoolElt, GrpSLPElt
- Example GrpPerm_RecogniseAltsym2 (H64E40)
- RecogniseSymmetric(G, n: parameters) : Grp, RngIntElt -> BoolElt, Map, Map, Map, Map, BoolElt
- SymmetricElementToWord (G, g) : Grp, GrpElt -> BoolElt, GrpSLPElt
- RecogniseAlternating(G, n: parameters) : Grp, RngIntElt -> BoolElt, Map, Map, Map, Map, BoolElt
- AlternatingElementToWord (G, g) : Grp, GrpElt -> BoolElt, GrpSLPElt
- GuessAltsymDegree(G: parameters) : Grp -> BoolElt, MonStgElt, RngIntElt
- Example GrpPerm_RecogniseAltsym2 (H64E41)
- Base and Strong Generating Set
- Construction of a Base and Strong Generating Set
- Defining Values for Attributes
- AssertAttribute(G, "Order", n) : GrpPerm, MonStgElt, RngIntElt ->
- AssertAttribute(G, "Order", Q) : GrpPerm, MonStgElt, [<RngIntElt, RngIntElt>] ->
- [Future release] AssertAttribute(G, "BSGS", S) : GrpPerm, MonStgElt, GrpPermBSGS ->
- Example GrpPerm_RandomSchreier (H64E44)
- Accessing the Base and Strong Generating Set
- Base(G) : GrpPerm -> [Elt]
- BasePoint(G, i) : GrpPerm, RngIntElt -> Elt
- BasicOrbit(G, i) : GrpPerm, RngIntElt -> SetIndx
- BasicOrbits(G) : GrpPerm -> [SetIndx]
- BasicOrbitLength(G, i) : GrpPerm, RngIntElt -> RngIntElt
- BasicOrbitLengths(G) : GrpPerm -> [RngIntElt]
- BasicStabilizer(G, i) : GrpPerm, RngIntElt -> GrpPerm
- BasicStabilizerChain(G) : GrpPerm -> [GrpPerm]
- IsMemberBasicOrbit(G, i, a) : GrpPerm, RngIntElt, Elt -> BoolElt
- NumberOfStrongGenerators(G) : GrpPerm -> RngIntElt
- NumberOfStrongGenerators(G, i) : GrpPerm, RngIntElt -> RngIntElt
- SchreierVectors(G) : GrpPerm -> [ [RngIntElt] ]
- SchreierVector(G, i) : GrpPerm, RngIntElt -> [RngIntElt]
- StrongGenerators(G) : GrpPerm -> SetIndx(GrpPermElt)
- StrongGenerators(G, i) : GrpPerm, RngIntElt -> SetIndx(GrpPermElt)
- Working with a Base and Strong Generating Set
- BaseImage(x) : GrpPermElt -> [Elt]
- Permutation(G, Q) : GrpPerm, [Elt] -> GrpPermElt
- SVPermutation(G, i, a) : GrpPerm, RngIntElt, Elt -> GrpPermElt
- SVWord(G, i, a) : GrpPerm, RngIntElt, Elt -> GrpFPElt
- Strip(H, x) : GrpPerm, GrpPermElt -> BoolElt, GrpPermElt, RngIntElt
- WordStrip(H, x) : GrpPerm, GrpPermElt -> BoolElt, GrpFPElt, RngIntElt
- BaseImageWordStrip(H, x) : GrpPerm, GrpPermElt -> BoolElt, GrpFPElt, RngIntElt
- WordInStrongGenerators(H, x) : GrpPerm, GrpPermElt -> GrpFPElt
- Modifying a Base and Strong Generating Set
- Permutation Representations of Linear Groups
- Permutation Group Databases
- Ordering of Permutation Groups
- Ordered Partition Stacks
- Construction of Ordered Partition Stacks
- Properties of Ordered Partition Stacks
- Degree(P) : StkPtnOrd -> RngIntElt
- Height(P) : StkPtnOrd -> RngIntElt
- NumberOfCells(P, h) : StkPtnOrd, RngIntElt -> RngIntElt
- CellNumber(P, h, x) : StkPtnOrd, RngIntElt, RngIntElt -> RngIntElt
- CellSize(P, h, i) : StkPtnOrd, RngIntElt, RngIntElt -> RngIntElt
- Cell(P, h, i): StkPtnOrd, RngIntElt, RngIntElt -> SeqEnum
- Random(P, i) : StkPtnOrd, RngIntElt -> RngIntElt
- Representative(P, i) : StkPtnOrd, RngIntElt -> RngIntElt
- ParentCell(P, i) : StkPtnOrd, RngIntElt -> RngIntElt
- Operations on Ordered Partition Stacks
- SplitCell(P, i, x) : StkPtnOrd, RngIntElt, RngIntElt -> BoolElt
- SplitAllByValues(P, V) : StkPtnOrd, SeqEnum[RngIntElt] -> BoolElt, RngIntElt
- SplitCellsByValues(P, C, V) : StkPtnOrd, SeqEnum[RngIntElt], SeqEnum[RngIntElt] -> BoolElt, RngIntElt
- Pop(P) : StkPtnOrd ->
- Advance(X, L, P, h) : StkPtnOrd, seqEnum[RngIntElt], StkPtnOrd, RngIntElt ->
- Example GrpPerm_OrderedPartitionStack (H64E46)
- Bibliography
V2.28, 13 July 2023