Definition:Group Action on Coset Space

Theorem
Let $G$ be a group.

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

The mapping $*: G \times G / H \to G / H$ by the rule:
 * $\forall g \in G, \forall g' H \in G / H: g * \paren {g' H} := \paren {g g'} H$

is the group action on the (left) coset space $G / H$.

Also see

 * Action of Group on Coset Space is Group Action