Cyclic subgroup

Definition

A cyclic subgroup is a generated subgroup, where the generating set is a single element of the group $(G,\times)$, that is:

• For any $g\in G$ the cyclic subgroup generated by $g$ is $\langle g\rangle$ (for the meaning of this notation see Generated subgroup)
• This is equivalent to $$\langle g\rangle=\{g^n\ |\ n\in\mathbb{Z}\}$$

This is a subgroup, and is Abelian (for finite groups - not sure about infinite)

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TODO: Proof of claims

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