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On Groups of Order \(pq\)

by Joseph A. Gallian (University of Minnesota, Duluth) and David Moulton (University of California, Berkeley)

This article originally appeared in:
Mathematics Magazine
October, 1995

Subject classification(s): Groups
Applicable Course(s): 4.2 Mod Algebra I & II

Without appeal to the Sylow theorem, the authors prove that, if \(p\) and \(q\) are primes with \(q < p\) and \(q\) does not divide \(p - 1\), then any group of order \(pq\) is cyclic.

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