Definition:Group Action Axioms

Let $\struct {G, \circ}$ be a group which acts on a set $X$.
The properties that define the group action $*: G \times X \to X$ are summarised as:
 $(GA \, 1)$ $:$ $\displaystyle \forall g, h \in G, x \in X:$ $\displaystyle g * \paren {h * x} = \paren {g \circ h} * x$ $(GA \, 2)$ $:$ $\displaystyle \forall x \in X:$ $\displaystyle e * x = x$