Definition:Conjugate Closure

Definition
Let $G$ be a group.

Let $S$ be a subset of $G$.

The conjugate closure of $S$ in $G$, denoted $\left\langle{S^G}\right\rangle$, is the subgroup of $G$ generated by $S^G$, where $S^G$ is the set of conjugates of $S$ in $G$:
 * $S^G = \left\{{g^{−1}sg: g \in G, s \in S}\right\}$

Also see

 * Normal Subgroup
 * Contranormal Subgroup


 * Normal Closure


 * Normal Closure is Conjugate Closure