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Mat. Zametki, 2017, Volume 101, Issue 2, Pages 211–214 (Mi mz10739)  

On Two Problems Related to Associators of Moufang Loops

I. B. Gorshkova, A. N. Grishkovb, A. V. Zavarnitsineac

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Universidade de São Paulo, Instituto de Matemática e Estatística
c Omsk State University

Abstract: A Moufang loop $M$ of order $3^{19}$ is constructed, together with a pair $a$$b$ of elements of $M$, such that the set of all elements of $M$ associating with $a$ and $b$ is not a subloop. This also gives an example of a nonassociative Moufang loop with a generating set in which every three elements have trivial associator.

Keywords: Moufang loop, associator, subloop.

Funding Agency Grant Number
Russian Foundation for Basic Research 13-01-00505
16-01-00577a
Fundação de Amparo à Pesquisa do Estado de São Paulo 2014/13730-0
The research of the first author was supported by the FAPESP Foundation (grant no. 2014/08964-1). The research of the second author was supported by the FAPESP and CNPq Foundations and by the Russian Foundation for Basic Research (under grant 16-01-00577a). The research of the third author was supported by the FAPESP Foundation and by the Russian Foundation for Basic Research (under grant 13-01-00505).

Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/mzm10739

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English version:
Mathematical Notes, 2017, 101:2, 230–233

Bibliographic databases:

UDC: 512.548.7
Received: 17.04.2015
Revised: 23.03.2016

Citation: I. B. Gorshkov, A. N. Grishkov, A. V. Zavarnitsine, “On Two Problems Related to Associators of Moufang Loops”, Mat. Zametki, 101:2 (2017), 211–214; Math. Notes, 101:2 (2017), 230–233

Citation in format AMSBIB
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