- Introduction
- Creation of a Cohomology Module
- CohomologyModule(G, M) : GrpPerm, ModGrp -> ModCoho
- CohomologyModule(G, Q, T) : GrpPerm, SeqEnum, SeqEnum -> ModCoho
- Example GrpCoh_coho-module1 (H74E1)
- Example GrpCoh_coho-module4 (H74E2)
- Example GrpCoh_coho-module2 (H74E3)
- Example GrpCoh_coho-module3 (H74E4)
- CohomologyModule(G, A, M) : GrpPerm, GrpAb, Any -> ModCoho
- Accessing Properties of the Cohomology Module
- Calculating Cohomology
- CohomologyGroup(CM, n) : ModCoho, RngIntElt -> ModTupRng
- Example GrpCoh_coho-module2cont (H74E6)
- Example GrpCoh_coho-module3cont (H74E7)
- CohomologicalDimension(CM, n) : ModCoho, RngIntElt -> RngIntElt
- CohomologicalDimension(M, n) : ModGrp, n -> RngIntElt
- CohomologicalDimensions(M, n) : ModGrp, n -> RngIntElt
- CohomologicalDimension(G, M, n) : GrpPerm, ModRng, RngIntElt -> RngIntElt
- H1Dimension(F, f, M) : GrpFP, Map, ModGrp -> RngIntElt
- H1Dimension(G, f, K) : GrpFP, Map, Rng -> RngIntElt
- H1DimensionSymmetricSquare(G, f, K) : GrpFP, Map, Rng -> RngIntElt
- Example GrpCoh_coho-example (H74E8)
- Example GrpCoh_coho-module4-cont (H74E9)
- Example GrpCoh_more-difficult (H74E10)
- Cocycles
- ZeroCocycle(CM, s) : ModCoho, SeqEnum -> UserProgram
- IdentifyZeroCocycle(CM, s) : ModCoho, UserProgram -> ModTupRngElt
- OneCocycle(CM, s) : ModCoho, SeqEnum -> UserProgram
- IdentifyOneCocycle(CM, s) : ModCoho, UserProgram -> ModTupRngElt
- IsOneCoboundary(CM, s) : ModCoho, UserProgram -> BoolElt, UserProgram
- TwoCocycle(CM, s) : ModCoho, SeqEnum -> UserProgram
- IdentifyTwoCocycle(CM, s) : ModCoho, UserProgram -> ModTupRngElt
- IsTwoCoboundary(CM, s) : ModCoho, UserProgram -> BoolElt, UserProgram
- Example GrpCoh_cocycles (H74E11)
- The Restriction to a Subgroup
- Other Operations on Cohomology Modules
- CorestrictionMapImage(G, C, c, i) : Grp, ModCoho, UserProgram, RngIntElt -> UserProgram
- InflationMapImage(M, c) : Map, UserProgram -> UserProgram
- CoboundaryMapImage(M, i, c) : ModCoho, RngIntElt, UserProgram -> UserProgram
- Constructing Extensions
- Extension(CM, s) : ModCoho, SeqEnum -> Grp, HomGrp, Map
- Extension(GrpPerm, CM, s) : Cat, ModCoho, SeqEnum -> GrpPerm, HomGrp, Map
- Example GrpCoh_A7cover (H74E13)
- Example GrpCoh_Dempwolff (H74E14)
- SplitExtension(CM) : ModCoho -> Grp, HomGrp, Map
- SplitExtension(G, M) : ModCoho -> Grp, ModGrp -> HomGrp, Map
- SplitExtension(GrpPerm,CM) : Cat, ModCoho -> GrpPerm, HomGrp, Map
- Example GrpCoh_split-extension (H74E15)
- Example GrpCoh_split-extension (H74E16)
- pMultiplicator(G, p) : GrpPerm, RngIntElt -> [ RngIntElt ]
- pCover(G, F, p) : GrpPerm, GrpFP, RngIntElt -> GrpFP
- Example GrpCoh_straightforward (H74E17)
- Example GrpCoh_nonsplit $2^5.L_5(2) (H74E18)
- Example GrpCoh_module-integers (H74E19)
- Constructing Distinct Extensions
- Finite Group Cohomology
- Creation of Gamma-groups
- GammaGroup(Gamma, A, action) : Grp, Grp, Map[Grp, GrpAuto] -> GGrp
- InducedGammaGroup(A, B) : GGrp, Grp -> GGrp
- Example GrpCoh_createGGrp (H74E24)
- IsNormalised(B, action) : Grp, Map -> BoolElt
- IsInduced(AmodB) : GGrp -> BoolElt, GGrp, GGrp, Map, Map
- Accessing Information
- One Cocycles
- OneCocycle(A, imgs) : GGrp, SeqEnum[GrpElt] -> OneCoC
- TrivialOneCocycle(A) : GGrp -> OneCoC
- IsOneCocycle(A, imgs) : GGrp, SeqEnum[GrpElt] -> BoolElt, OneCoC
- AreCohomologous(alpha, beta) : OneCoC, OneCoC -> BoolElt, GrpElt
- CohomologyClass(alpha) : OneCoC -> SetIndx[OneCoC]
- InducedOneCocycle(AmodB, alpha) : GGrp, OneCoC -> OneCoC
- ExtendedOneCocycle(alpha) : OneCoC -> SetEnum[OneCoC]
- ExtendedCohomologyClass(alpha) : OneCoC -> SetEnum[OneCoC]
- GammaGroup(alpha) : OneCoC -> GGrp
- CocycleMap(alpha) : OneCoC -> Map
- Group Cohomology
- Bibliography
V2.28, 13 July 2023