On two problems related to associators of Moufang loops

I. B. Gorshkov; A. N. Grishkov; A. V. Zavarnitsine

doi:10.1134/S0001434617010278

On two problems related to associators of Moufang loops

作者: Gorshkov I.B.¹, Grishkov A.N.²^,3, Zavarnitsine A.V.¹
隶属关系:
1. Sobolev Institute of Mathematics
2. Instituto de Matemática e Estatística
3. Dostoevskii Omsk State University
期: 卷 101, 编号 1-2 (2017)
页面: 230-233
栏目: Volume 101, Number 2, February, 2017
URL: https://journals.rcsi.science/0001-4346/article/view/149984
DOI: https://doi.org/10.1134/S0001434617010278
ID: 149984

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详细

A Moufang loop M of order 3¹⁹ 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.