Normal subgroup in which every subgroup characteristic in the whole group is characteristic

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This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: normal subgroup and subgroup in which every subgroup characteristic in the whole group is characteristic
View other subgroup property conjunctions | view all subgroup properties

Definition

A subgroup $K$ of a group $G$ is termed a normal subgroup in which every subgroup characteristic in the whole group is characteristic if $K$ is a normal subgroup of $G$ and every subgroup $H$ of $K$ that is a characteristic subgroup of $G$ is also a characteristic subgroup of $K$.

Relation with other properties

Stronger properties

• Direct factor
• Normal AEP-subgroup

Weaker properties

• Subgroup in which every subgroup characteristic in the whole group is characteristic