Abelian characteristic subgroup

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

Definition

Symbol-free definition

A subgroup of a group is termed an Abelian characteristic subgroup if it is Abelian as a group and characteristic as a subgroup.

Relation with other properties

Stronger properties

• Cyclic characteristic subgroup

Weaker properties

• Abelian normal subgroup
• Nilpotent characteristic subgroup