G-module

In the context of algebra, particularly in representation theory and module theory, a **G-module** is a module that is equipped with an action by a group \( G \). Specifically, if \( G \) is a group and \( M \) is a module over a ring \( R \), a \( G \)-module is a set \( M \) together with a group action of \( G \) on \( M \) that is compatible with the operation of \( M \).