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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A simplified proof of Moufang's theorem


Author: Aleš Drápal
Journal: Proc. Amer. Math. Soc. 139 (2011), 93-98
MSC (2010): Primary 20N05; Secondary 08A05
Published electronically: July 21, 2010
MathSciNet review: 2729073
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Abstract: Moufang's theorem states that if $ Q$ is a Moufang loop with elements $ x$, $ y$ and $ z$ such that $ x\cdot yz = xy \cdot z$, then these three elements generate a subgroup of $ Q$. The paper contains a new proof of this theorem that is shorter and more transparent than the standardly used proof of Bruck.


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Additional Information

Aleš Drápal
Affiliation: Department of Mathematics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic
Email: drapal@karlin.mff.cuni.cz

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10501-4
PII: S 0002-9939(2010)10501-4
Keywords: Moufang loops, Moufang’s theorem
Received by editor(s): December 31, 2009
Received by editor(s) in revised form: March 12, 2010
Published electronically: July 21, 2010
Additional Notes: The author was supported by the Grant Agency of Czech Republic, grant 201/09/0296.
Communicated by: Jonathan I. Hall
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.