Definition:Order of Group Element/Finite

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

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

If there exists $k \in \Z_{> 0}$ such that $x^k = e_G$, then $x$ is of finite order, or has finite order.

Also known as
An element of finite order is also known as a torsion element.

Also see

 * Definition:Torsion Subgroup
 * Definition:Torsion Element of Module