Cyclic group
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A group G is cyclic if it is generated by a single element <math>a \in G</math>, i.e., <math>G = \{a^n, n \in \mathbb{Z} \}</math>.
Every cyclic group is commutative. Any group with a prime number of elements is cyclic. A cyclic group is either isomorphic to <math>\mathbb{Z}</math> , or to <math>\mathbb{Z}/n\mathbb{Z}</math> for some <math>n \in \mathbb{N}</math>.