Sylow's theorem for Moufang loops

TL;DR

This paper extends Sylow's theorems to finite Moufang loops, establishing criteria for p-Sylow subloops and analyzing their maximal orders in loops lacking such subloops.

Contribution

It provides the first Sylow theorem analog for Moufang loops and characterizes the maximal order of p-subloops without p-Sylow subloops.

Findings

Established a criterion for the existence of p-Sylow subloops in finite Moufang loops.

Determined the maximal order of p-subloops in loops without p-Sylow subloops.

Extended classical Sylow theorems from groups to 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.