Abstract
It has been proven by F. Leong and the author (1997, J. Algebra190, 474–486) that all Moufang loops of order pαqα11···qαnn are associative if p and qi are odd primes with p<q1<···<qn, and•(i)α≤3, α≤2; or•(ii)≥5, α≤4, α≤2.In this paper, we prove the existence of nonassociative Moufang loops of order pq3 for every pair of odd primes, p and q with q≡1(modp).
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