Definition:Group Action/Right Group Action

Definition
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:

Also see

 * Definition:Opposite Group


 * Definition:Left Group Action