Category:Definitions/Conjugacy Action

This category contains definitions related to Conjugacy Action.
Related results can be found in Category:Conjugacy Action.

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:

$\forall x, g \in G: x * g = g^{-1} \circ x \circ g$