Action of Group on Coset Space is Group Action

Theorem
Let $$G$$ be a group whose identity is $$e$$.

Let $$H$$ be a subgroup of $$G$$.

Then $$G$$ is a group action on the left coset space $$G/H$$ by the rule:
 * $$\forall g \in G: g * H = g H$$

Proof
As $$H$$ is a subset of $$G$$, the result follows from Group Action on Subset of Group.