Conjugacy-distinguished element

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This article defines a property of elements in groups

Definition

An element g in a group G is termed conjugacy-distinguished if whenever h is an element of G not conjugate to g, there exists a normal subgroup of finite index N \le G, such that the images of g and h under the quotient map G \to G/N are not conjugate in G/N.

A group where every element is conjugacy-distinguished is termed a conjugacy-separable group.