Compatibility in certain quasigroup homogeneous space.
type: Item
instance of: scholarly article
zbMATH Open document ID: 1291.20064
DOI: 10.4134/BKMS.2013.50.2.667
author: Bokhee Im
author: Ji-Young Ryu
published in: Bulletin of the Korean Mathematical Society
publication date: 2013-10-31T00:00:00Z
full work available at URL: http://www.mathnet.or.kr/mathnet/kms_content.php
Mathematics Subject Classification ID: 20N05
Mathematics Subject Classification ID: 05C69
Mathematics Subject Classification ID: 20B99
zbMATH DE Number: 6221363
zbMATH Keywords: quasigroups
zbMATH Keywords: Latin squares
zbMATH Keywords: action matrices
zbMATH Keywords: quasigroup actions
zbMATH Keywords: homogeneous spaces
zbMATH Keywords: approximate symmetries
MaRDI profile type: Publication
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title: Compatibility in certain quasigroup homogeneous space.
review text: The authors consider in this paper a special double-cover \(Q\) of the symmetric group of degree 3. They show that a proper non-regular approximate symmetry occurs from its quasigroup homogeneous space. They consider a quasigroup obtained by permuting entries in the multiplication table of the direct product \(S_3\times Z_2\) of the symmetric group \(S_3\) with the 2-element additive group \(Z_2\) of integers modulo 2, as in [\textit{B. Im} et al., J. Algebr. Comb. 33, No. 1, 81-93 (2011; Zbl 1214.20062)], where the authors consider the general development of the theory of quasigroup permutation representations. In the present paper they want to establish a non-regular approximate symmetry from a quasigroup homogeneous space of degree 4. In Theorem 3.3, p. 673, the authors completely characterize the weak compatibility of any two elements of quasigroup \(Q\). However, the strong compatibility of \(Q\) still remains open. But the authors expect to characterize the compatibility completely for the case of degree 6, in which case the homogeneous space is uniform. For details see [loc. cit.].
reviewed by: C. Pereira da Silva
description: scientific article; zbMATH DE number 6221363