Cyclic group

Revision as of 12:37, 10 May 2008 by Boy Soprano II (talk | contribs) (New page: A '''cyclic group''' <math>G</math> is a group generated by a single element. Some sources add the stipluation that <math>G</math> be finite. The term '''monogenous group''', however, ge...)
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A cyclic group $G$ is a group generated by a single element. Some sources add the stipluation that $G$ be finite. The term monogenous group, however, generally means any group generated by a single element. The distinction is somewhat small, as all infinite monogenous groups are isomorphic to the integers $\mathbb{Z}$ under addition. All other cyclic groups are of the form $\mathbb{Z}/n\mathbb{Z}$, for some positive integer $n$.

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