Definition:Order of Group Element/Definition 2

Definition
Let $G$ be a group whose identity is $e_G$.

Let $x \in G$ be an element of $G$.

The order of $x$ (in $G$), denoted $\order x$, is the order of the group generated by $x$:
 * $\order x := \order {\gen x}$

Also see

 * Equivalence of Definitions of Order of Group Element