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The restricted Burnside problem for Moufang loops

Part of: Other generalizations of groups Other nonassociative rings and algebras

Published online by Cambridge University Press:  16 July 2021

ALEXANDER GRISHKOV ,
LIUDMILA SABININA  and
EFIM ZELMANOV
ALEXANDER GRISHKOV
Affiliation:
Department of Mathematics, University of São Paulo, Caixa Postal 66281, São Paulo-SP, 05311-970, Brazil. Omsk F.M. Dostoevsky State University, Neftezavodskaya 11, Omsk, Omskaya obl., 644053, Russia. e-mail: grishkov@ime.usp.br
LIUDMILA SABININA*
Affiliation:
Department of Mathematics, Autonomous University of the State of Morelos, Avenida Universidad 1001, Cuernavaca, 62209 Morelos, Mexico. e-mail: liudmila@uaem.mx
EFIM ZELMANOV
Affiliation:
Department of Mathematics, University of California, San Diego, 9500 Giman Dr. La Jolla, California 92093-0112, U.S.A. e-mail: ezelmanov@math.ucsd.edu
*
†Corresponding author
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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 $p^n$.

MSC classification

Primary: 20N05: Loops, quasigroups
Secondary: 17D10: Mal'cev (Mal'tsev) rings and algebras

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 173 , Issue 1 , July 2022 , pp. 201 - 211
Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Cambridge Philosophical Society

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Footnotes

Dedicated to the memory of Peter Plaumann

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