Normal-isomorph-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]

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Definition

Definition with symbols

A subgroup $H$ of a group $G$ is termed a normal-isomorph-containing subgroup if $H$ is a normal subgroup of $G$, and for any normal subgroup $K$ of $G$ isomorphic to $H$, $K$ is contained in $H$.

Relation with other properties

Stronger properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
Normal-isomorph-free subgroup	normal and no other isomorphic normal subgroup			|FULL LIST, MORE INFO
Isomorph-containing subgroup	contains every isomorphic subgroup of whole group			|FULL LIST, MORE INFO
Isomorph-free subgroup	no other isomorphic subgroup			|FULL LIST, MORE INFO