# Conjugacy-determined subgroup

## Contents

BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]
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.
View other such properties

## Definition

Suppose $H \le K \le G$ are groups. We say that $H$ is conjugacy-determined in $K$ relative to $G$, or that $K$ contains fusion of elements of $H$ in $G$, if two elements of $H$ are conjugate in $K$ if and only if they are conjugate in $G$.

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