Sylow's theorem for Moufang loops

Abstract

For finite Moufang loops, we prove an analog of the first Sylow theorem giving a criterion of the existence of a p-Sylow subloop. We also find the maximal order of p-subloops in the Moufang loops that do not possess p-Sylow subloops.

21 pages

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• Radicals and embeddings of Moufang loops in alternative loop algebras