Order has only two prime factors implies solvable for Moufang loops

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ANALOGY: This is an analogue in Moufang loops of a fact encountered in group. The old fact is: order has only two prime factors implies solvable.
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Statement

Suppose L is a finite Moufang loop (i.e., a Moufang loop whose underlying set is finite). Suppose the order (i.e., the size of the underlying set) of L has at most two distinct prime factors, i.e., it is of the form p^aq^b where p,q are primes and a,b are nonnegative integers (possibly zero). Then, L is a Solvable Moufang loop (?) (and in particular a finite solvable Moufang loop).

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