Axiom:Right Group Action Axioms

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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:

\((\text {RGA} 1)\)   $:$     \(\ds \forall g, h \in G, x \in X:\) \(\ds \paren {x * g} * h = x * \paren {g \circ h} \)      
\((\text {RGA} 2)\)   $:$     \(\ds \forall x \in X:\) \(\ds x * e = x \)      

These properties can be referred to as the right group action axioms.