# Conjugacy-determined subgroup

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This article describes a property that can be evaluated for a triple of a group, a subgroup of the group, and a subgroup of that subgroup.

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## Definition

Suppose are groups. We say that is **conjugacy-determined** in relative to , or that contains fusion of elements of in , if two elements of are conjugate in if and only if they are conjugate in .

If is conjugacy-determined in itself relative to , is termed a conjugacy-closed subgroup of .