Moufang Loops of Odd Order $p_1p_2\cdots p_nq^3$
Bulletin of the Malaysian Mathematical Society, Tome 34 (2011) no. 2 Cet article a éte moissonné depuis la source Bulletin of the Malaysian Mathematical Society website

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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 $p_1p_2\cdots p_nq^3$.
Classification : 20N05.
@article{BMMS_2011_34_2_a15,
     author = {Andrew Rajah and Wing Loon Chee},
     title = {Moufang {Loops} of {Odd} {Order} \(p_1p_2\cdots p_nq^3\)},
     journal = {Bulletin of the Malaysian Mathematical Society},
     year = {2011},
     volume = {34},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/BMMS_2011_34_2_a15/}
}
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Andrew Rajah; Wing Loon Chee. Moufang Loops of Odd Order \(p_1p_2\cdots p_nq^3\). Bulletin of the Malaysian Mathematical Society, Tome 34 (2011) no. 2. http://geodesic.mathdoc.fr/item/BMMS_2011_34_2_a15/