# Definition Given an [[Group Element|element]] $g$ of a finite [[group]] $G$, where the [[Group Element Order|order]] of $g$ is $n$, then the cyclic subgroup of $g$, $\langle g \rangle$ is $ \{e, g, g^2, \ldots, g^{n-1}\} $ Note that $|\langle g \rangle| = |g|$. This subgroup is [[Abelian Group|abelian]].