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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