Definition:Order of Group Element/Finite/Definition 2

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

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

$x$ is of finite order, or has finite order if and only if there exist $m, n \in \Z_{> 0}$ such that $m \ne n$ but $x^m = x^n$.

Also known as

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

Also see