\begin{definition}[Definition:Generated Normal Subgroup/Definition 2]
Let $G$ be a group. 
Let $S \subseteq G$ be a subset.
The '''normal subgroup generated by $S$''', denoted $\gen {S^G}$, is the subgroup generated by the set of conjugates of $S$:
:$\gen {S^G} = \set {g^{−1}sg: g \in G, s \in S}$
\end{definition}