Definition:Order of Group Element/Finite/Definition 1
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Definition
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 exists $k \in \Z_{> 0}$ such that $x^k = e_G$.
Also known as
An element of finite order of $G$ is also known as a torsion element of $G$.
Also see
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): order: 6. (of a group or element)
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): order: 6. (of a group or element)