Group Acts on Itself

Theorem
Let $\struct {G, \circ}$ be a group whose identity is $e$.

Then $\struct {G, \circ}$ acts on itself by the rule:


 * $\forall g, h \in G: g * h = g \circ h$

Proof
Follows directly from the group axioms and the definition of a group action.

Also see

 * Stabilizer of Element of Group Acting on Itself is Trivial
 * Orbit of Element of Group Acting on Itself is Group