On Moufang Loops of Odd Order pq2 Original Research Article

It is known that all Moufang loops of order p, p2, pq, and p3 are groups when p and q are primes [O. Chein, Trans. Amer. Math. Soc.188, No. 2 (1974), 31-35]. Are Moufang loops of odd order pqr and pq2 associative for distinct primes p, q, and r? M. Purtill [J. Algebra112 (1988), 122-128] gave an affirmative answer. However, a flaw was discovered in the proof for the case pq2 where p < q [M. Purtill, J. Algebra145 (1992), 262]. In this paper, we prove that the conjecture is still true.