Creation of a Cohomology Module
CohomologyModule(G, M) : GrpPerm, ModGrp -> ModCoho
CohomologyModule(G, invar, mats) : GrpPerm, SeqEnum, SeqEnum -> ModCoho
Example GrpCoh_coho-module1 (H23E1)
Accessing Properties of the Cohomology Module
Module(CM) : ModCoho -> ModGrp
Invariants(CM) : ModCoho -> SeqEnum
Dimension(CM) : ModCoho -> RngIntElt
Ring(CM) : ModCoho -> ModGrp
Group(CM) : ModCoho -> Grp
FPGroup(CM) : ModCoho -> Grp, HomGrp
Calculating Cohomology
CohomologyGroup(CM, n) : ModCoho, RngIntElt -> ModTupRng
CohomologicalDimension(CM, n) : ModCoho, RngIntElt -> RngIntElt
CohomologicalDimension(G, M, n) : GrpPerm, ModRng, RngIntElt -> RngIntElt
Example GrpCoh_coho-example (H23E2)
Example GrpCoh_more-difficult (H23E3)
Cocycles
ZeroCocycle(CM, s) : ModCoho, SeqEnum -> ModTupRngElt
IdentifyZeroCocycle(CM, s) : ModCoho, SeqEnum -> ModTupRngElt
OneCocycle(CM, s) : ModCoho, SeqEnum -> UserProgram
IdentifyOneCocycle(CM, s) : ModCoho, ModTupRngElt -> UserProgram
TwoCocycle(CM, s) : ModCoho, SeqEnum -> ModTupRngElt
IdentifyTwoCocycle(CM, s) : ModCoho, UserProgram -> ModTupRngElt
Example GrpCoh_cocylces (H23E4)
Extensions with Prescribed Action
Extension(CM, s) : ModCoho, SeqEnum -> Grp
SplitExtension(CM) : ModCoho -> Grp
DistinctExtensions(CM) : ModCoho -> SeqEnum
pMultiplicator(G, p) : GrpPerm, RngIntElt -> [ RngIntElt ]
pCover(G, F, p) : GrpPerm, GrpFP, RngIntElt -> GrpFP
Example GrpCoh_straightforward (H23E5)
Example GrpCoh_module-integers (H23E6)
Extensions without Prescribed Action
ExtensionsOfElementaryAbelianGroup(p, d, G) : RngIntElt, RngIntElt, GrpPerm -> SeqEnum
ExtensionsOfSolubleGroup(H, G) : GrpPerm, GrpPerm -> SeqEnum