AoPSWiki
Do you have what it takes to be the next brilliant trader, researcher, or developer at Jane Street Capital? Find out in the Careers in Mathematics Forum.
Personal tools

Cyclic group

From AoPSWiki

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.

This article is a stub. Help us out by expanding it.

Looking for a challenging algebra text? Preparing for MATHCOUNTS or the AMC exams?
Check out Art of Problem Solving's Introduction to Algebra by Richard Rusczyk.
© Copyright 2008 AoPS Incorporated. All Rights Reserved. • FoundationPrivacyContact Us