- Introduction
- Finding Elements with Prescribed Properties
- Monte Carlo Algorithms for Subgroups
- CentraliserOfInvolution(G, g : parameters) : GrpMat,GrpMatElt -> GrpMat
- CentraliserOfInvolution(G, g, w : parameters) : GrpMat,GrpMatElt, GrpSLPElt -> GrpMat, []
- AreInvolutionsConjugate(G, x, wx, y, wy : parameters) : GrpMat,GrpMatElt, GrpSLPElt, GrpMatElt, GrpSLPElt -> BoolElt, GrpMatElt, GrpSLPElt
- NormalClosureMonteCarlo(G, H ) : GrpMat, GrpMat -> GrpMat
- DerivedGroupMonteCarlo(G : parameters) : GrpMat -> GrpMat
- IsProbablyPerfect(G : parameters): Grp -> BoolElt
- Example GrpMatFF_IsProbablyPerfect (H66E1)
- Aschbacher Reduction
- Constructive Recognition for Simple Groups
- Constructive Recognition for Classical Groups
- ClassicalStandardGenerators(type, d, q) : MonStgElt, RngIntElt, RngIntElt -> []
- ClassicalConstructiveRecognition(G, type, d, q) : GrpMat[FldFin], MonStgElt, RngIntElt, RngIntElt ->BoolElt, Map, Map, Map, Map, SeqEnum, SeqEnum
- Example GrpMatFF_ClassicalConstructiveRecognition (H66E10)
- ClassicalChangeOfBasis(G): GrpMat[FldFin] -> GrpMatElt[FldFin]
- ClassicalRewrite(G, gens, type, dim, q, g : parameters): Grp, SeqEnum, MonStgElt, RngIntElt, RngIntElt, GrpElt -> BoolElt, GrpElt
- ClassicalRewriteNatural(type, CB, g): MonStgElt, GrpMatElt, GrpMatElt-> BoolElt, GrpElt
- ClassicalStandardPresentation (type, d, q : parameters) : MonStgElt, RngIntElt, RngIntElt -> SLPGroup, []
- Example GrpMatFF_ClassicalConstructiveRecognition (H66E11)
- Constructive Recognition for Exceptional Groups
- ExceptionalStandardGenerators(type, rank, q) : MonStgElt, RngIntElt, RngIntElt -> []
- ExceptionalConstructiveRecognition(G, type, rank, q) : GrpMat[FldFin], MonStgElt, RngIntElt, RngIntElt ->BoolElt, Map, Map, Map, Map, SeqEnum, SeqEnum
- Example GrpMatFF_ExceptionalConstructiveRecognition (H66E12)
- ExceptionalRewrite(type, rank, q, X, Xm, g): MonStgElt, RngIntElt, RngIntElt,SeqEnum, SeqEnum, GrpElt -> BoolElt, GrpElt
- ExceptionalStandardPresentation (type, rank, q) : MonStgElt, RngIntElt, RngIntElt -> SLPGroup, []
- Example GrpMatFF_exp_standard (H66E13)
- Composition Trees for Matrix Groups
- The Composition Tree Algorithm
- Constructing the Composition Tree
- Accessing the Composition Tree
- CompositionTreeOrder(G) : Grp -> RngIntElt
- CompositionTreeNonAbelianFactors(G) : Grp -> RngIntElt
- DisplayCompTreeNodes(G : parameters) : Grp ->
- Example GrpMatFF_CompTreeJ4 (H66E16)
- CompositionTreeNiceGroup(G) : Grp -> GrpMat[FldFin]
- CompositionTreeSLPGroup(G) : Grp -> GrpSLP, Map
- CompositionTreeNiceToUser(G) : Grp -> Map, []
- CompositionTreeOrder(G) : Grp -> RngIntElt
- CompositionTreeElementToWord(G, g) : Grp, GrpElt -> BoolElt, GrpSLPElt
- CompositionTreeNonAbelianFactors(G) : GrpMat[FldFin] -> List
- CompositionTreeCBM(G) : GrpMat[FldFin -> GrpMatElt
- CompositionTreeReductionInfo(G, t) : Grp, RngIntElt -> MonStgElt,Grp, Grp
- CompositionTreeSeries(G) : Grp -> SeqEnum, List, List, List, BoolElt, []
- CompositionTreeFactorNumber(G, g) : Grp, GrpElt -> RngIntElt
- HasCompositionTree(G) : Grp -> BoolElt
- CleanCompositionTree(G) : Grp ->
- Example GrpMatFF_CompTree1 (H66E17)
- Example GrpMatFF_CompTree2 (H66E18)
- The LMG functions
- SetLMGSchreierBound(n) : RngIntElt ->
- LMGInitialize(G : parameters) : GrpMat ->
- LMGOrder(G) : GrpMat[FldFin] -> RngIntElt
- LMGFactoredOrder(G) : GrpMat[FldFin] -> SeqEnum
- LMGIsIn(G, x) : GrpMat, GrpMatElt -> BoolElt, GrpSLPElt
- LMGIsSubgroup(G, H) : GrpMat, GrpMat -> BoolElt
- LMGEqual(G, H) : GrpMat, GrpMat -> BoolElt
- LMGIndex(G, H) : GrpMat, GrpMat -> RngIntElt
- LMGIsNormal(G, H) : GrpMat, GrpMat -> BoolElt
- LMGNormalClosure(G, H) : GrpMat, GrpMat -> GrpMat
- LMGDerivedGroup(G) : GrpMat -> GrpMat
- LMGCommutatorSubgroup(G, H) : GrpMat, GrpMat -> GrpMat
- LMGIsSoluble(G) : GrpMat -> BoolElt
- LMGIsNilpotent(G) : GrpMat -> BoolElt
- LMGCompositionSeries(G) : GrpMat[FldFin] -> SeqEnum
- LMGCompositionFactors(G) : GrpMat[FldFin] -> SeqEnum
- LMGChiefSeries(G) : GrpMat[FldFin] -> SeqEnum
- LMGChiefFactors(G) : GrpMat[FldFin] -> SeqEnum
- LMGUnipotentRadical(G) : GrpMat -> GrpMat, GrpPC, Map
- LMGSolubleRadical(G) : GrpMat -> GrpMat, GrpPC, Map
- LMGFittingSubgroup(G) : GrpMat -> GrpMat, GrpPC, Map
- LMGCentre(G) : GrpMat -> GrpMat
- LMGSylow(G,p) : GrpMat, RngIntElt -> GrpMat
- LMGSocleStar(G) : GrpMat -> GrpMat
- LMGSocleStarFactors(G) : GrpMat -> SeqEnum, SeqEnum
- LMGSocleStarAction(G) : GrpMat -> Map, GrpPerm, GrpMat
- LMGSocleStarActionKernel(G) : GrpMat -> GrpMat, GrpPC, Map
- LMGSocleStarQuotient(G) : GrpMat -> GrpPerm, Map, GrpMat
- Example GrpMatFF_LMGex (H66E19)
- LMGRadicalQuotient(G) : GrpMat -> GrpPerm, Map, GrpMat
- LMGCentraliser(G, g) : GrpMat, GrpMatElt -> GrpMat
- LMGIsConjugate(G, g, h) : GrpMat, GrpMatElt, GrpMatElt -> BoolElt, GrpMatElt
- LMGClasses(G) : GrpMat -> SeqEnum
- LMGNormaliser(G, H) : GrpMat, GrpMat -> GrpMat
- LMGIsConjugate(G, H, K) : GrpMat, GrpMat, GrpMat -> BoolElt, GrpMatElt
- LMGMeet(G, H, K) : GrpMat, GrpMat, GrpMat -> GrpMat
- LMGMaximalSubgroups(G) : GrpMat -> SeqEnum
- LMGNormalSubgroups(G) : GrpMat -> SeqEnum
- LMGLowIndexSubgroups(G,n) : GrpMat, RngIntElt -> SeqEnum
- LMGCosetAction(G,H : parameters) : GrpMat, GrpMat -> Map, GrpPerm, GrpMat
- LMGCosetImage(G,H) : GrpMat, GrpMat -> GrpPerm
- LMGCosetActionInverseImage(G, f, i) : GrpMat, Map, RngIntElt -> GrpMatElt
- LMGRightTransversal(G,H : parameters) : GrpMat, GrpMat -> SeqEnum
- LMGIsPrimitive(G) : GrpMat -> BoolElt
- LMGCharacterTable(G : parameters) : GrpMat -> SeqEnum
- Example GrpMatFF_LMGex2 (H66E20)
- Finding a Base
- Unipotent Matrix Groups
- Bibliography
V2.28, 13 July 2023