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A Moufang loop's commutant
Published online by Cambridge University Press: 08 December 2011
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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