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A Characterization of Infinite Cyclic Groups

by Charles Lanski

This article originally appeared in:
Mathematics Magazine
February, 2001

Subject classification(s): Algebra and Number Theory | Abstract Algebra | Groups
Applicable Course(s): 4.2 Mod Algebra I & II

The theorem, “An infinite group is cyclic when each of its nonidentity subgroups have finite index,” is proved and discussed, and a test to show groups are not cyclic is  presented.

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