Normal-homomorph-containing subgroup

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This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

Definition

A subgroup N of a group G is termed normal-homomorph-containing if N is a normal subgroup of G, and for any homomorphism \varphi:N \to G such that \varphi(N) is also a normal subgroup of G, we have \varphi(N) \le N.

Relation with other properties

Stronger properties

Weaker properties