Axiom:Right Group Action Axioms

Definition

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.

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