Normal-subhomomorph-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 normal subgroup N of a group G is termed a normal-subhomomorph-containing subgroup if, for any subgroup H of N and any homomorphism of groups \varphi:H \to G such that \varphi(H) is a normal subgroup of G, \varphi(H) is contained in N.

Relation with other properties

Stronger properties

Weaker properties