\begin{definition}[Definition:Group Action/Right Group Action]
Let $X$ be a set.
Let $\struct {G, \circ}$ be a group whose identity is $e$.
A '''right group action''' is a mapping $\phi: X \times G \to X$ such that:
:$\forall \tuple {x, g} \in X \times G : x * g := \map \phi {x, g} \in X$
in such a way that the right group action axioms are satisfied:
{{:Definition:Right Group Action Axioms}}
\end{definition}