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We show that if L is a finite Moufang loop and p is a “Sylow prime” for L then there exists a Sylow p -subloop of L . Moreover, if L 1 is a p -subloop of L then L 1 is contained in a Sylow p -subloop of L . Finally, for finite Moufang loops that don't contain Sylow p -subloops, any p -subloop can be embedded in some quasi-Sylow p -subloop.
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