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Lagrange's theorem for Moufang loops

Published online by Cambridge University Press:  22 June 2005

ALEXANDER N. GRISHKOV  and
ANDREI V. ZAVARNITSINE
ALEXANDER N. GRISHKOV
Affiliation:
Departamento de Matemática, Universidade de São Paulo, Caixa Postal 66281, São Paulo-SP, 05311-970, Brasil, and Omsk State University, pr. Mira 55-a, 644077, Russia. e-mail: [email protected]
Supported by FAPESP and CNPq, Brazil.
ANDREI V. ZAVARNITSINE
Affiliation:
Sobolev Institute of Mathematics, pr. Koptyuga 4, Novosibirsk, 630090, Russia and Departamento de Matemática, Universidade de São Paulo, Caixa Postal 66281, São Paulo-SP, 05311-970, Brasil. e-mail: [email protected]
Supported by FAPESP, Brazil, and RAS, Russia.
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Abstract

We prove that the order of any subloop of a finite Moufang loop is a factor of the order of the loop, thus obtaining an analog of Lagrange's theorem for finite Moufang loops.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 139 , Issue 1 , July 2005 , pp. 41 - 57
Copyright
2005 Cambridge Philosophical Society

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