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A Moufang loop's commutant

Published online by Cambridge University Press:  08 December 2011

STEPHEN M. GAGOLA III
STEPHEN M. GAGOLA III*
Affiliation:
Department of Mathematics, The University of Arizona, 617 N. Santa Rita Ave, Tucson, AZ 85721-0089, U.S.A. e-mail: sgagola@math.arizona.edu
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Abstract

The commutant of a loop is the set of elements which commute with all of the elements in the loop. The commutant of a Moufang loop is a subloop, but it has been an open problem to classify the Moufang loops for which the commutant is normal. It was S. Doro [3] who conjectured that a Moufang loop, under certain conditions, has a normal commutant. We settle this conjecture here by proving that the commutant of any Moufang loop is always a normal subloop.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 152 , Issue 2 , March 2012 , pp. 193 - 206
Copyright
Copyright © Cambridge Philosophical Society 2011

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References

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