Cyclic group

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A group G is cyclic if it is generated by a single element $a\in G$ , i.e., $G=\{a^{n},n\in \mathbb {Z} \}$ .

Every cyclic group is commutative. Any group with a prime number of elements is cyclic. A cyclic group is either isomorphic to $\mathbb {Z}$ , or to $\mathbb {Z} /n\mathbb {Z}$ for some $n\in \mathbb {N}$ .

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