Definition:Conjugate (Group Theory)/Subset/Also defined as

Definition
Let $\struct {G, \circ}$ be a group.

Let $S \subseteq G, a \in G$.

The $G$-conjugate of $S$ by $a$ is:
 * $S^a := \set {y \in G: \exists x \in S: y = a^{-1} \circ x \circ a} = a^{-1} \circ S \circ a$

Also see

 * Conjugate of Set by Group Product.