Moufang loops of even order
\textit{O. Chein} [Trans. Am. Math. Soc. 188, No. 2, 31-51 (1974; Zbl 0263.20007)] and \textit{M. Purtill} [J. Algebra 112, 122-128 (1988; Zbl 0644.20040)] investigated Moufang loops \(L\) of even order \(n\) and proved that \(L\) are groups if \(n = 2^ k\) \((0 \leq k \leq 4)\) or \(n = 2p\) (\(p\) is any prime) or \(n = 2p^ 2\). In this paper the authors give necessary and sufficient conditions for all Moufang loops of order \(2m\) to be groups.
scientific article; zbMATH DE number 562443