Cyclic group

A cyclic group $G$ is a group generated by a single element. Some sources add the stipluation that $G$ be finite. The term monogenous group, however, generally means any group generated by a single element. The distinction is somewhat small, as all infinite monogenous groups are isomorphic to the integers $\mathbb{Z}$ under addition. All other cyclic groups are of the form $\mathbb{Z}/n\mathbb{Z}$, for some positive integer $n$.

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