Hall's Theorem for Moufang loops

A loop K is solvable if there exists a normal series 1=K0⊴K1⊴K2⊴⋯⊴Kn=K of subloops Ki such that each factor Ki/Ki−1 is an abelian group. Back in 1966, G. Glauberman proved [G. Glauberman, On loops of odd order II, J. Algebra 8 (1968) 393–414] that every Moufang loop of odd order is solvable. He also showed that if π is any set of primes then every Moufang loop of odd order contains a Hall π-subloop. Since then it has been an open question whether or not P. Hall's Theorem holds for all finite Moufang loops. Here we affirmatively answer this question by showing that a finite Moufang loop is solvable if and only if it contains a Hall π-subloop for any set of primes π.