Normal complex of groups

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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}.

Relation with other properties

Stronger properties

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

Weaker properties

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