Moufang Loops of Odd Order p4q13 ... qn3

It has been proven that all Moufang loops of order p4q3 where p and q are odd primes with 3 < p < q are associative if and only if q = 1(mod p). Also all Moufang loops of order p3 1 p3 2 center dot center dot center dot p3 n where each pi are a prime with 3 = p1 < p2 center dot center dot center dot < pn were proven to be associative if and only if pi = 1(mod pj). In this paper, we extend these results to Moufang loops of order p4q3 1q3 2 center dot center dot center dot q3 n where p and each qi is a prime with 3 < p < q1 < q2 center dot center dot center dot < qn, qi = 1(mod p) and qi = 1(mod q(j)).