Moufang Loops of Odd Order pmq1 ... qn

AbstractLet 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