\begin{definition}[Definition:Conjugate (Group Theory)/Subset/Also defined as]
Let $\struct {G, \circ}$ be a group.
Let $S \subseteq G, a \in G$.
The '''$G$-conjugate of $S$ by $a$''' is:
:$S^a := \set {y \in G: \exists x \in S: y = a^{-1} \circ x \circ a} = a^{-1} \circ S \circ a$
\end{definition}