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