Definition:Group Action/Right Group Action

Definition
Let $X$ be a set.

Let $\left({G, \circ}\right)$ be a group whose identity is $e$.

A right group action is an mapping $\phi: X \times G \to X$ such that:


 * $\forall \left({x, g}\right) \in G \times X: x * g := \phi \left({\left({x, g}\right)}\right) \in X$

in such a way that the right group action axioms are satisfied:

Also see

 * Definition:Opposite Group