Moufang loops of odd order \(p^ mq_ 1\ldots q_ n\) (Q1335073)

This paper establishes by neat inductive arguments that if \(p\) and \(q_ 1, q_ 2, q_ 3,\dots\) are odd prime numbers with \(p < q_ i\) for all \(i\), then a Moufang loop of order \(p^ n q_ 1 \dots q_ n\) is a group when \(m = 1, 2\) or 3. The result for \(m = 1\) is obtained from a result of \textit{M. Purtill} [J. Algebra 112, 122-128 (1988; Zbl 0644.20040)]. All three results are dependent on the work of \textit{G. Glauberman} [J. Algebra 8, 393-414 (1968; Zbl 0155.039)].