\begin{definition}[Definition:Order of Group Element/Definition 2]
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 $x$:
:$\order x := \order {\gen x}$
\end{definition}