# On Groups of Order $pq$

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

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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