Definition:Group Action/Left Group Action

Definition
Let $X$ be a set.

Let $\struct {G, \circ}$ be a group whose identity is $e$.

A (left) group action is an operation $\phi: G \times X \to X$ such that:


 * $\forall \tuple {g, x} \in G \times X: g * x := \map \phi {g, x} \in X$

in such a way that the group action axioms are satisfied:

Also see

 * Definition:Right Group Action