Definition:Conjugacy Action/Subsets

Definition
Let $G$ be a group. Let $\powerset G$ be the power set of $G$.

The (left) conjugacy action on subsets is the group action $* : G \times \powerset G \to \powerset G$:
 * $g * S = g \circ S \circ g^{-1}$

The right conjugacy action on subsets is the group action $* : \powerset G \times G \to \powerset G$:
 * $S * g = g^{-1} \circ S \circ g$

Also see

 * Conjugacy Action is Group Action