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Zbl 1192.20061
Rajah, Andrew; Chong, Kam-Yoon
Moufang loops of odd order $p_1p_2\cdots p_nq^3$ with non-trivial nucleus. (English)
[J] Commentat. Math. Univ. Carol. 49, No. 2, 301-307 (2008). ISSN 0010-2628

Let $p_i$ and $q$ be primes such that $2<p_1<p_2<\cdots<q$ and $q\not\equiv 1\pmod{p_i}$ and $p_i\not\equiv 1\pmod{p_j}$. Let $L$ be a Moufang loop of order $p_1p_2\cdots p_nq^3$. The authors prove that if the nucleus of $L$ is non-trivial then $L$ is a group. Besides of this, the paper comprises a number of known results on Moufang loops connected with groups.
[Ivan Chajda (Přerov)]

MSC 2000:: *20N05 Loops (group theory)

Keywords: nonassociative Moufang loops; orders of finite loops

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