In mathematics, given a group G {\displaystyle G} , a G-module is an abelian group M {\displaystyle M} on which G {\displaystyle G} acts compatibly with the abelian group structure on M {\displaystyle M} . This widely applicable notion generalizes that of a representation of G. Group (co)homology provides an important set of tools for studying general G {\displaystyle G} -modules.
In mathematics, given a group G {\displaystyle G} , a G-module is an abelian group M {\displaystyle M} on which G {\displaystyle G} acts compatibly with the abelian group structure on M {\displaystyle M} . This widely applicable notion generalizes that of a representation of G. Group (co)homology provides an important set of tools for studying general G {\displaystyle G} -modules.
Source: Wikipedia "G-module" · CC BY-SA 4.0
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