Abstract
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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