The **order** of an element $g$ in a multiplicative group $G$ is the least positive integer $n$ such that $g^n$ is the identity element of $G$, if such an integer exist, and is $\infty$ otherwise. In an additive group, the order of $g$ is the least positive integer $n$ such that $ng=0$. In both cases, the order of $g$ is also equal to the cardinality of the cyclic subgroup it generates.

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- Review status: reviewed
- Last edited by Andrew Sutherland on 2020-10-12 08:20:25

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- 2020-10-12 08:20:25 by Andrew Sutherland (Reviewed)
- 2020-10-12 07:03:19 by John Cremona
- 2020-10-12 06:59:11 by John Cremona
- 2020-10-12 06:57:54 by John Cremona

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