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 .

Last modified on 18 November 2008, at 00:10
# Cyclic group

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 .