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Acknowledgements
Introduction
Low Level Operations on Presentations and Words
Modifying Presentations
Low Level Operations on Words
Interactive Coset Enumeration
Introduction
Constructing and Modifying a Coset Enumeration Process
Starting and Restarting an Enumeration
Accessing Information
Induced Permutation Representations
Coset Spaces and Transversals
p-Quotients (Process Version)
The p-Quotient Process
Using p-Quotient Interactively
Soluble Quotients
Introduction
Construction
Calculating the Relevant Primes
The Functions
Soluble Quotient Processes
Initialisation
Access Functions
Symbolic Collector
Relevant Primes
Irreducible Modules
Extension Spaces
Lifting a Quotient
Lifting a Quotient by Choosing an Individual Cocycle
Soluble Quotient Process Tools
Checking the soluble quotient
Tools for the calculation of specific normal series
Miscellaneous Functions
Calculation of Standard Sections
Bibliography
DETAILS
Introduction
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 (H62E1)
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 (H62E2)
Interactive Coset Enumeration
Introduction
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 (H62E3)
Example GrpFP_2_ACEProc2 (H62E4)
Example GrpFP_2_ACEProc3 (H62E5)
Example GrpFP_2_ACEProc4 (H62E6)
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 (H62E7)
Example GrpFP_2_ACEProcCosetSpace (H62E8)
p-Quotients (Process Version)
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 (H62E9)
Example GrpFP_2_pQuotient6 (H62E10)
Example GrpFP_2_pQuotient7 (H62E11)
Example GrpFP_2_pQuotient8 (H62E12)
Soluble Quotients
Introduction
Construction
Calculating the Relevant Primes
The Functions
SolubleQuotient(F, n : parameters): GrpFP, RngIntElt -> GrpPC, Map, SeqEnum, MonStgElt
Soluble Quotient Processes
Initialisation
Initialize(F) : GrpFP -> SQProc
Initialize(e) : Map -> SQProc
SolubleQuotientProcess(F : parameters): GrpFP -> SQProc
Access Functions
PrintQuotient(SQP) : SQProc ->
GetQuotient(SQP) : SQProc -> GrpPC, Map
PrintCollector(SQP) : SQProc ->
PrintPrimes(SQP) : SQProc ->
GetPrimes(SQP) : SQProc -> SetEnum, BoolElt
PrintModules(SQP) : SQProc ->
GetModules(SQP, p ) : SQProc, RngIntElt -> List
PrintExtensions(SQP) : SQProc ->
PrintRelat(SQP) : SQProc ->
GetParent(SQP) : SQProc -> List
GetChildren(SQP) : SQProc -> List
GetChild(SQP, i) : SQProc, RngIntElt -> List
PrintSeries(SQP) : SQProc ->
PrintProcess(SQP) : SQProc ->
Symbolic Collector
NonsplitCollector(SQP, p) : SQProc, RngIntElt ->
DeleteCollector(SQP, p) : SQProc, RngIntElt ->
DeleteCollector(SQP) : SQProc, RngIntElt ->
Relevant Primes
Primes(SQP): SQProc ->
AddPrimes(SQP, p): SQProc, RngIntElt ->
ReplacePrimes(SQP, m): SQProc, SetEnum ->
Irreducible Modules
Modules(SQP : parameters): SQProc ->
Extension Spaces
SplitExtensionSpace(SQP): SQProc -> SeqEnum
NonsplitExtensionSpace(SQP): SQProc -> SeqEnum
DeleteSplitSolutionspace(SQP, p, i, k): SQProc, RngIntElt, RngIntElt, RngIntElt ->
Lifting a Quotient
LiftSplitExtension(SQP, p, i, k : parameters) : SQProc, RngIntElt, RngIntElt, RngIntElt -> RngIntElt, SQProc
LiftSplitExtensionRow(SQP): SQProc -> RngIntElt, SQProc
LiftNonsplitExtension(SQP, p, i, k : parameters) : SQProc, RngIntElt, RngIntElt, RngIntElt -> RngIntElt, SQProc
LiftNonsplitExtensionRow(SQP, p, l) : SQProc, RngIntElt, RngIntElt -> RngIntElt, SQProc
Lifting a Quotient by Choosing an Individual Cocycle
Soluble Quotient Process Tools
Checking the soluble quotient
SQ_check(SQP) : SQProc -> BoolElt
EquivalentQuotients(SQP, SQR : parameters) : SQProc, SQProc -> BoolElt, SQProc
Tools for the calculation of specific normal series
KeepPrimePower(SQP, p) : SQProc, RngIntElt -> SeqEnum
KeepGeneratorOrder(SQG, SQH) : SQProc, SQProc -> SeqEnum
KeepGeneratorAction(SQG, SQH) : SQProc, SQProc -> SeqEnum
KeepSplit(SQG, SQH) : SQProc, SQProc -> SeqEnum
KeepElementary(SQG, SQH) : SQProc, SQProc -> SeqEnum
KeepAbelian(SQG, SQH) : SQProc, SQProc -> SeqEnum
KeepElementaryAbelian(SQG, SQH) : SQProc, SQProc -> SeqEnum
[Future release] KeepDirect(SQG, SQH) : SQProc, SQProc -> SeqEnum
KeepSplitAbelian(SQG, SQH) : SQProc, SQProc -> SeqEnum
KeepSplitElementaryAbelian(SQG, SQH) : SQProc, SQProc -> SeqEnum
Miscellaneous Functions
IntersectKernels(SQP, SQR) : SQProc, SQProc -> SQProc, Map, Map
ComposeQuotients(SQ1, SQ2, SQ3: parameter) : SQProc, SQProc, SQProc -> BoolElt, SQProc
Calculation of Standard Sections
AbelianSection(SQP: parameter) : SQProc -> BoolElt, SQProc
ElementaryAbelianSection(SQP: parameter) : SQProc -> BoolElt, SQProc
SplitSection(SQP: parameter) : SQProc -> BoolElt, SQProc
SplitAbelianSection(SQP: parameter) : SQProc -> BoolElt, SQProc
SplitElementaryAbelianSection(SQP: parameter) : SQProc -> BoolElt, SQProc
NonsplitSection(SQP: parameter) : SQProc -> BoolElt, SQProc
NilpotentSection(SQP: parameter) : SQProc -> BoolElt, SQProc
Bibliography
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