Definition:Conjugacy Action

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

The (left) conjugacy action of $G$ is the left group action $* : G \times G \to G$ defined as:
 * $\forall g, x \in G: g * x = g \circ x \circ g^{-1}$

The right conjugacy action of $G$ is the right group action $* : G \times G \to G$ defined as:
 * $\forall x, g \in G: x * g = g^{-1} \circ x \circ g$

Also known as
Some sources refer to this group action of $g * x$ as the transform of $x$ by $g$.

Also see

 * Conjugacy Action is Group Action