Conjugacy-separable group

Definition
A group is termed conjugacy-separable if it satisfies the following equivalent conditions:


 * 1) Every element in it is a defining ingredient::conjugacy-distinguished element.
 * 2) Given any two elements in it that are not conjugate, there exists a finite quotient group where their images are also not conjugate.
 * 3) It is a defining ingredient::residually finite group and, under the natural embedding into its profinite completion (note that the map is an embedding because it is residually finite), the group is a conjugacy-closed subgroup of the profinite completion.

Stronger properties

 * Weaker than::Finite group

Weaker properties

 * Stronger than::Residually finite group:

Facts

 * Conjugacy-closed subgroup of conjugacy-separable group is conjugacy-separable