\begin{definition}[Definition:Conjugate Closure]
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 $G$:
:$S^G = \left\{{g^{−1}sg: g \in G, s \in S}\right\}$
\end{definition}