Group Action on Coset Space

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.

$\blacksquare$

Sources

• Allan Clark: Elements of Abstract Algebra (1971)... (previous)... (next): $\S 53$