Normal complex of groups

Definition

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

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

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

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
chain complex of abelian groups	all the groups are abelian	follows from abelian implies every subgroup is normal		\|FULL LIST, MORE INFO

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
chain complex of groups				\|FULL LIST, MORE INFO