Moufang Loops of Odd Order $p_1p_2\cdots p_nq^3$
Bulletin of the Malaysian Mathematical Society, Tome 34 (2011) no. 2
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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/}
}
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/