Normal complex of groups

Definition

A chain complex of groups $(G_{n},d_{n})_{n\in \mathbb {Z} }$ given as follows:

$\dots \to G_{n}{\stackrel {d_{n}}{\to }}G_{n-1}{\stackrel {d_{n-1}}{\to }}G_{n-2}\to \dots$

is termed a normal complex of groups if, for every $n\in \mathbb {Z}$, the image group $d_{n}(G_{n})$ is a normal subgroup inside $G_{n-1}$.