# Abelian conjugacy-closed subgroup

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

## Definition

### Definition with symbols

A subgroup  of a group  is termed an Abelian conjugacy-closed subgroup if it satisfies the following equivalent conditions:

• No two distinct elements of  are conjugate in .
•  is an Abelian group, and is conjugacy-closed as a subgroup: if any two elements of  are conjugate in , they are conjugate in .