\begin{definition}[Definition:Right Group Action Axioms]
Let $\struct {G, \circ}$ be a group which acts on a set $X$.
The properties that define the right group action $*: X \times G \to X$ are summarized as:
{{begin-axiom}}
{{axiom | n = \text {RGA} 1
        | q = \forall g, h \in G, x \in X
        | m = \paren {x * g} * h = x * \paren {g \circ h}
}}
{{axiom | n = \text {RGA} 2
        | q = \forall x \in X
        | m =  x * e = x
}}
{{end-axiom}}
These properties can be referred to as the '''right group action axioms'''.
Category:Definitions/Group Actions
\end{definition}