Moufang Loops of Odd Order pmq1 … qn Original Research Article

Let L be a Moufang loop of odd order L = pmql…qn. Is L a group? This question has been affirmatively answered by Chein for L = p, p2, p3 and pq where p and q are distinct odd primes [2]. Purtill has also shown that L is a group if L = pqr and L = p2q where p, q, r are distinct odd primes with p < q [5]. We shall show that L is a group if L = pmql … qn where p and all the q are distinct odd primes with p < qi and 1 ≤ m ≤ 3.