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.

Examples

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

Relation with other properties

Stronger properties

• Cyclic characteristic subgroup
• Characteristic central subgroup
• Abelian critical subgroup
• Maximal among Abelian characteristic subgroups

Weaker properties

• Abelian normal subgroup
• Class two characteristic subgroup
• Nilpotent characteristic subgroup

Related group properties

• Group in which every Abelian characteristic subgroup is central