Abstract
AbstractThe 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.
Publisher
Cambridge University Press (CUP)
Cited by
6 articles.
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1. Some Varieties of Loops (Bol-Moufang and Non-Bol-Moufang Types);Algebra without Borders – Classical and Constructive Nonassociative Algebraic Structures;2023
2. On Doro’s conjecture for finite Moufang loops;International Journal of Algebra and Computation;2022-11-08
3. Characterization of Moufang loops whose commutant is a normal subloop;Journal of Group Theory;2022-03-03
4. Moufang loops with nonnormal commutative centre;Mathematical Proceedings of the Cambridge Philosophical Society;2020-01-10
5. On the non-commuting graph in finite Moufang loops;Journal of Algebra and Its Applications;2018-04