 Group extension

A group extension of $G$ by an abelian $G$-module $A$ is a short exact sequencewhose conjugation action on $A$ is the specified $G$-action.

Group extension is a concept in group theory, a branch of abstract algebra. It refers to the process of creating a new group from a known group by adding new elements that satisfy certain properties related to the original group. More formally, it describes a way to construct a group \( G \) that contains a normal subgroup \( N \) and a quotient group \( G/N \).