Difference between revisions of "Cyclic group"
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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 to <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 to <math>\mathbb{Z}/n\mathbb{Z}</math> for some <math>n \in \mathbb{N}</math>. | ||
| + | [[Category:Algebra]] | ||
Latest revision as of 00:10, November 18, 2008
A group G is cyclic if it is generated by a single element , i.e., .
Every cyclic group is commutative. Any group with a prime number of elements is cyclic. A cyclic group is either isomorphic to , or to for some .
