Definition:Order of Group Element

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

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

Also known as
Some sources call this the period of the element.

Also denoted as
The order of an element $g \in G$ is sometimes seen as $o \left({g}\right)$.

Some sources render it as $\operatorname{Ord} \left({g}\right)$.

Also see

 * Equivalence of Definitions of Order of Group Element


 * Equal Powers of Group Element implies Finite Order