# Definition:Group Action on Coset Space

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## Definition

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

• Results about the group action on a coset space can be found here.