# Order has only two prime factors implies solvable for Moufang loops

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.

View other analogues of order has only two prime factors implies solvable|View other analogues from group to Moufang loop (OR, View as a tabulated list)

## Statement

Suppose 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 has at most two distinct prime factors, i.e., it is of the form where are primes and are nonnegative integers (possibly zero). Then, is a Solvable Moufang loop (?) (and in particular a finite solvable Moufang loop).