Volume 34 • Number 2 • 2011   • Moufang Loops of Odd Order \(p_1p_2\cdots p_nq^3\) Andrew Rajah and Wing Loon Chee Abstract. It has been proved that for distinct odd primes \(p_1,p_2,\ldots,p_n\) and \(q\), all Moufang loops of order \(p_1p_2\cdots p_nq^3\) are associative if:     (1). \(q\not\equiv1\pmod {p_1}\) and for each \(i>1\), \(q^2\not\equiv1\pmod {p_i}\); or     (2). \(p_1 < p_2 < \cdots < p_n < q\), \(q \not\equiv1 \pmod {p_i}\), \(p_i \not\equiv1 \pmod {p_j}\) for all \(i,j\), and the nucleus is not trivial. In this paper, we extend these results by giving a complete resolution for Moufang loops of odd order \(p_1p_2\cdots p_nq^3\). 2010 Mathematics Subject Classification: 20N05. Full text: PDF