Low Level Operations on Presentations and Words
Modifying Presentations
AddGenerator(G) : GrpFP -> GrpFP
AddGenerator(G, w) : GrpFP, GrpFPElt -> GrpFP
AddRelation(G, r) : GrpFP, RelElt -> GrpFP
AddRelation(G, g) : GrpFP, GrpFPElt -> GrpFP
AddRelation(G, r, i) : GrpFP, RelElt, RngIntElt -> GrpFP
AddRelation(G, g, i) : GrpFP, GrpFPElt, RngIntElt -> GrpFP
DeleteGenerator(G, x) : GrpFP, GrpFPElt -> GrpFP
DeleteRelation(G, r) : GrpFP, RelElt -> GrpFP
DeleteRelation(G, g) : GrpFP, GrpFPElt -> GrpFP
DeleteRelation(G, i) : GrpFP, RngIntElt -> GrpFP
ReplaceRelation(G, s, r) : GrpFP, RelElt, RelElt -> GrpFP
ReplaceRelation(G, i, r) : GrpFP, RngIntElt, RelElt -> GrpFP
ReplaceRelation(G, i, g) : GrpFP, RngIntElt, GrpFPElt -> GrpFP
Example GrpFP_2_Replace (H71E1)
Low Level Operations on Words
Eliminate(u, x, v) : GrpFPElt, GrpFPElt, GrpFPElt -> GrpFPElt
Eliminate(U, x, v) : { GrpFPElt }, GrpFPElt, GrpFPElt -> { GrpFPElt }
Match(u, v, f) : GrpFPElt, GrpFPElt, RngIntElt -> BoolElt, RngIntElt
RotateWord(u, n) : GrpFPElt, RngIntElt -> GrpFPElt
Substitute(u, f, n, v) : GrpFPElt, RngIntElt, RngIntElt, GrpFPElt -> GrpFPElt
Subword(u, f, n) : GrpFPElt, RngIntElt, RngIntElt -> GrpFPElt
Example GrpFP_2_WordOps (H71E2)
Constructing and Modifying a Coset Enumeration Process
CosetEnumerationProcess(G, H: parameters) : GrpFP, GrpFP -> GrpFPCosetEnumProc
AddRelator(~P, w) : GrpFPCosetEnumProc, GrpFPElt ->
AddSubgroupGenerator(~P, w) : GrpFPCosetEnumProc, GrpFPElt ->
SetProcessParameters(~P: parameters) : GrpFPCosetEnumProc ->
Starting and Restarting an Enumeration
StartEnumeration(~P: parameters) : GrpFPCosetEnumProc ->
RedoEnumeration(~P: parameters) : GrpFPCosetEnumProc ->
CanRedoEnumeration(P) : GrpFPCosetEnumProc -> BoolElt
ContinueEnumeration(~P: parameters) : GrpFPCosetEnumProc ->
CanContinueEnumeration(P) : GrpFPCosetEnumProc -> BoolElt
ResumeEnumeration(~P: parameters) : GrpFPCosetEnumProc ->
Accessing Information
CosetsSatisfying(P : parameters) : GrpFPCosetEnumProc -> { GrpFPElt }
CosetTable(P) : GrpFPCosetEnumProc -> Map
HasValidCosetTable(P) : GrpFPCosetEnumProc -> BoolElt
HasClosedCosetTable(P) : GrpFPCosetEnumProc -> BoolElt
ExcludedConjugate(P) : GrpFPCosetEnumProc -> GrpFPElt
ExistsCosetSatisfying(P : parameters) : GrpFPCosetEnumProc -> BoolElt, GrpFPElt
ExistsExcludedConjugate(P) : GrpFPCosetEnumProc -> BoolElt, GrpFPElt
ExistsNormalisingCoset(P) : GrpFPCosetEnumProc -> BoolElt, GrpFPElt
Group(P) : GrpFPCosetEnumProc -> GrpFP
Index(P) : GrpFPCosetEnumProc -> RngIntElt
HasValidIndex(P) : GrpFPCosetEnumProc -> BoolElt
MaximalNumberOfCosets(P) : GrpFPCosetEnumProc -> RngIntElt
Subgroup(P) : GrpFPCosetEnumProc -> GrpFP
TotalNumberOfCosets(P) : GrpFPCosetEnumProc -> RngIntElt
Example GrpFP_2_ACEProc1 (H71E3)
Example GrpFP_2_ACEProc2 (H71E4)
Example GrpFP_2_ACEProc3 (H71E5)
Example GrpFP_2_ACEProc4 (H71E6)
Induced Permutation Representations
CosetAction(P) : GrpFPCosetEnumProc -> Map, GrpPerm, GrpFP
CosetImage(P) : GrpFPCosetEnumProc -> GrpPerm
CosetKernel(P) : GrpFPCosetEnumProc -> GrpFP
Coset Spaces and Transversals
CosetSpace(P) : GrpFPCosetEnumProc -> GrpFPCos
RightCosetSpace(P) : GrpFPCosetEnumProc -> GrpFPCos
Transversal(P) : GrpFPCosetEnumProc -> {@ GrpFPElt @}, Map
Example GrpFP_2_ACEProcTransversal (H71E7)
Example GrpFP_2_ACEProcCosetSpace (H71E8)
The p-Quotient Process
pQuotientProcess(F, p, c: parameters) : GrpFP, RngIntElt, RngIntElt -> Process
NextClass(~P : parameters) : GrpPCpQuotientProc ->
Using p-Quotient Interactively
StartNewClass(~P: parameters) : GrpPCpQuotientProc ->
Tails(~P: parameters) : GrpPCpQuotientProc ->
Consistency(~P: parameters) : GrpPCpQuotientProc ->
CollectRelations(~P) : GrpPCpQuotientProc ->
ExponentLaw(~P : parameters) : GrpPCpQuotientProc ->
EliminateRedundancy(~P) : GrpPCpQuotientProc ->
Display(P) : GrpPCpQuotientProc ->
RevertClass(~P) : GrpPCpQuotientProc ->
pCoveringGroup(~P) : GrpPCpQuotientProc ->
GeneratorStructure(P) : GrpPCpQuotientProc ->
Jacobi(~P, c, b, a, ~r) : GrpPCpQuotientProc, RngIntElt, RngIntElt, RngIntElt -> RngIntElt ->
Collect(P, Q) : GrpPCpQuotientProc, [ <RngIntElt, RngIntElt> ] -> [ RngIntElt ] ->
EcheloniseWord(~P, ~r) : GrpPCpQuotientProc -> RngIntElt
SetDisplayLevel(~P, Level) : GrpPCpQuotientProc, RngIntElt ->
ExtractGroup(P) : GrpPCpQuotientProc -> GrpPC
Order(P) : GrpPCpQuotientProc -> RngIntElt
FactoredOrder(P) : GrpPCpQuotientProc -> [ <RngIntElt, RngIntElt> ]
NumberOfPCGenerators(P) : GrpPCpQuotientProc -> RngIntElt
pClass(P) : GrpPCpQuotientProc -> RngIntElt
NuclearRank(G) : GrpPC -> RngIntElt
pMultiplicatorRank(G) : GrpPC -> RngIntElt
Example GrpFP_2_pQuotient5 (H71E9)
Example GrpFP_2_pQuotient6 (H71E10)
Example GrpFP_2_pQuotient7 (H71E11)
Example GrpFP_2_pQuotient8 (H71E12)
Calculating the Relevant Primes
The Functions
SolubleQuotient(F, n : parameters): GrpFP, RngIntElt -> GrpPC, Map, SeqEnum, MonStgElt
Bibliography
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Version: V2.19 of
Wed Apr 24 15:09:57 EST 2013