The Restricted Burnside Problem for Moufang Loops

TL;DR

This paper proves that for certain primes and parameters, only finitely many finite Moufang loops exist with a given number of generators and exponent, advancing understanding of their algebraic structure.

Contribution

It establishes the finiteness of m-generated Moufang loops of a fixed prime power exponent for primes not equal to 2 or 3.

Findings

Finiteness of m-generated Moufang loops for specified parameters

Results apply to primes p ≠ 2,3

Advances the understanding of Moufang loop classification

Abstract

We prove that for positive integers $m \geq 1, n \geq 1$ and a prime number $p \neq 2,3$ there are finitely many finite $m$-generated Moufang loops of exponent $p^n$.