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Moufang loops with nonnormal commutative centre

Part of: Other generalizations of groups

Published online by Cambridge University Press:  10 January 2020

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, Brazil. e-mail: grishkov@ime.usp.br
ANDREI V. ZAVARNITSINE
Affiliation:
Sobolev Institute of Mathematics, 4, Koptyug av., Novosibirsk, 630090, Russia. e-mail: zav@math.nsc.ru
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Abstract

We construct two infinite series of Moufang loops of exponent 3 whose commutative centre (i. e. the set of elements that commute with all elements of the loop) is not a normal subloop. In particular, we obtain examples of such loops of orders 38 and 311 one of which can be defined as the Moufang triplication of the free Burnside group B(3, 3).

MSC classification

Primary: 20N05: Loops, quasigroups
Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 170 , Issue 3 , May 2021 , pp. 609 - 614
Copyright
© Cambridge Philosophical Society 2020

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Footnotes

†

Supported by the program of fundamental scientific research of SB RAS No. I.1.1., project No. 0314-2016-0001 and by FAPESP, process 2017/14489-2.

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