Representation theory of groups | Group theory

G-module

In mathematics, given a group G, a G-module is an abelian group M on which G acts compatibly with the abelian group structure on 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-modules. The term G-module is also used for the more general notion of an R-module on which G acts linearly (i.e. as a group of R-module automorphisms). (Wikipedia).

G-module
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Group representation | Automorphism | Continuous function | Topological group | Group (mathematics) | Group cohomology | Binary quadratic form | Quotient group | Group ring | Abelian category | Mathematics | Function (mathematics) | Field (mathematics) | Integer | Special linear group | Group homomorphism | Matrix multiplication | Abelian group | Product topology | Module (mathematics)