Normal subgroup whose automorphism group is abelian

This article describes a property that arises as the conjunction of a subgroup property: normal subgroup with a group property (itself viewed as a subgroup property): aut-abelian group
View a complete list of such conjunctions

Statement

A subgroup $H$ of a group $G$ is termed an aut-abelian normal subgroup of $G$ if it satisfies both these conditions:

• $H$ is a normal subgroup of $G$.
• $H$ is an aut-abelian group: the automorphism group $\mathrm{A}\mathrm{u}\mathrm{t}(H)$ is an abelian group.

Relation with other properties

Stronger properties

• Cyclic normal subgroup

Weaker properties

• Class two normal subgroup