Hall's theorem for Moufang loops. (Q984427)

\textit{G. Glauberman} showed, [in J. Algebra 8, 393-414 (1968; Zbl 0155.03901)], that if \(L\) is finite Moufang loop of odd order, then \(L\) is solvable and that for any set of primes, \(\pi\), \(L\) contains a Hall \(\pi\)-subloop. Since 1968 it has been an open question whether or not Hall's theorem holds for all finite Moufang loops. In this paper the author answers this question affirmatively by showing that a finite Moufang loop is solvable if and only if it contains a Hall \(\pi\)-subloop for any set of primes \(\pi\). Furthermore, if we know that \(L\) is solvable and that either 3, or \(2\in\pi\), then \(\pi\)-subloops of \(L\) embed in some Hall \(\pi\)-subloop of \(L\).