---
tag: AEW7V6ZSZA
kind: concept
name: G-module
aliases: [module-over-a-group, zg-module]
sources:
  - wikipedia: en:26068776@r1320979952
    locator: G-module
    note: adopted
    mention: wikipedia://en/26068776
    sections: [Summary]
same_as:
  wikidata: Q2912125
  wikipedia: G-module
inventory: [61E3Q205ZZ]
---

## Summary

In mathematics, given a group $G$, a ***G*-module** is an [[abelian group|071DDFVG4J]] $M$ 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.