Moufang loops of odd order \(p^ 4q_ 1\dots q_ n\) (Q1922896)

It was proved by \textit{F. Leong, P. E. Teh}, and \textit{V. K. Lim} [J. Algebra 168, No. 1, 348-352 (1994; Zbl 0814.20054)] that all Moufang loops of odd order \(p^\alpha q_1\dots q_n\) are groups for \(\alpha\leq 3\), where \(p\), \(q_1,\dots,q_n\) are odd primes with \(p<q_i\). In the paper mentioned above, the authors raised the question whether their result also holds for \(\alpha=4\). For \(p=3\), the answer is negative since, by a well known classical result, there exist nonassociative Moufang loops of order \(3^4\). In the paper under review, the authors now give an affirmative answer for \(p\geq 5\). They remark that there is no hope of extending this result to odd order with \(\alpha=5\) since there exist nonassociative Moufang loops of order \(p^5\).