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Possible orders of nonassociative Moufang loops

Orin Chein; Andrew Rajah — 2000

Commentationes Mathematicae Universitatis Carolinae

The paper surveys the known results concerning the question: “For what values of $n$ does there exist a nonassociative Moufang loop of order $n$ ?” Proofs of the newest results for $n$ odd, and a complete resolution of the case $n$ even are also presented.

Moufang loops of odd order $p_{1} p_{2} \dots p_{n} q^{3}$ with non-trivial nucleus

Andrew Rajah; Kam-Yoon Chong — 2008

Commentationes Mathematicae Universitatis Carolinae

It has been proven by F. Leong and the first author (J. Algebra (1997), 474–486) that all Moufang loops of order $p^{α} q_{1}^{β_{1}} q_{2}^{β_{2}} \cdot \cdot \cdot q_{n}^{β_{n}}$ where $p$ and $q_{i}$ are odd primes, are associative if $p < q_{1} < q_{2} < \cdot \cdot \cdot < q_{n}$ , and (i) $α \leq 3$ \alpha \le 3 ...

Moufang loops of odd order $p_{1} p_{2} \dots p_{n} q^{3}$ .

Rajah, Andrew; Chee, Wing Loon — 2011

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

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Possible orders of nonassociative Moufang loops

Moufang loops of odd order p 1 p 2 ⋯ p n q 3 with non-trivial nucleus

Moufang loops of odd order p 1 p 2 ⋯ p n q 3 .

Moufang loops of odd order $p_{1} p_{2} \dots p_{n} q^{3}$ with non-trivial nucleus

Moufang loops of odd order $p_{1} p_{2} \dots p_{n} q^{3}$ .