# 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.

$\blacksquare$