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New page: 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...
A [[Group (mathematics)|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 [[Isomorphism|isomorphic]] to <math>\mathbb{Z}</math> , or tp <math>\mathbb{Z}/n\mathbb{Z}</math> for some <math>n \in \mathbb{N}</math>.
Every cyclic group is [[commutative]]. Any group with a [[prime number]] of elements is cyclic. A cyclic group is either [[Isomorphism|isomorphic]] to <math>\mathbb{Z}</math> , or tp <math>\mathbb{Z}/n\mathbb{Z}</math> for some <math>n \in \mathbb{N}</math>.