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Accessing Properties of the Cohomology Module

The functions described in this section merely return data used to define the cohomology module. In each case, the argument CM must be a cohomology module returned by a call to CohomologyModule.

Module(CM) : ModCoho -> ModGrp
The K[G]-module used to define the cohomology module CM. An error occurs if CM was defined by an action on a finitely generated abelian group.
Invariants(CM) : ModCoho -> SeqEnum
Given a cohomology module CM that was defined by an action on a finitely generated abelian group A, return the invariants of A. If CM was not defined by an action on an abelian group, an error results.
Dimension(CM) : ModCoho -> RngIntElt
Let CM be a cohomology module. If CM was defined by the action of a group on an R-module M, return the dimension of M. In the case in which CM was defined by the action of a group on a finitely generated abelian group A, the rank of A is returned.
Ring(CM) : ModCoho -> ModGrp

The ring over which the module used to define the cohomology module CM is defined. If CM is defined in terms of an action on a finitely generated abelian group A, then the ring will be the integers if A is infinite, and the integers modulo the exponent of A if A is finite.

Group(CM) : ModCoho -> Grp
The group used to define action on the cohomology module CM.
FPGroup(CM) : ModCoho -> Grp, HomGrp
Given a cohomology module CM with associated group G, return a finitely presented group F isomorphic to G and the isomorphism from F to G. This presentation is on a strong generating set if G is a permutation or matrix group. It is used in the construction of presentations of extensions returned by the function Extension.
MatrixOfElement(CM, g) : ModCoho, GrpElt -> AlgMatElt
The matrix representing the action of the element g in the group of CM on the module of CM.
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Version: V2.19 of Wed Apr 24 15:09:57 EST 2013