Transitively normal subgroup of normal 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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This page describes a subgroup property obtained as a composition of two fundamental subgroup properties: transitively normal subgroup and normal subgroup
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Definition

Definition with symbols

A subgroup $H$ of a group $G$ is termed a transitively normal subgroup of normal subgroup if there exists a subgroup $K$ of $G$ containing $H$ such that $K$ is a normal subgroup of $G$ and $H$ is a transitively normal subgroup of $K$ .

Relation with other properties

Stronger properties

Weaker properties

2-subnormal subgroup