\(2\)-perfect \(m\)-cycle systems can be equationally defined for \(m=3\), \(5\), and \(7\) only
type: Item
instance of: scholarly article
title: \(2\)-perfect \(m\)-cycle systems can be equationally defined for \(m=3\), \(5\), and \(7\) only
zbMATH Open document ID: 0855.05039
DOI: 10.1007/BF01190966
published in: Algebra Universalis
publication date: 1996-02-25T00:00:00Z
review text: A natural quasigroup associated with a 2-perfect \(m\)-cycle system is examined, and it is shown that except when the cycle length \(m\) is 3, 5, or 7, the 2-perfect \(m\)-cycle systems cannot be equationally defined. The proof proceeds by producing a quasigroup associated with a 2-perfect \(m\)-cycle system, for which a particular homomorphic image does not arise from a 2-perfect \(m\)-cycle system.
reviewed by: Charles J. Colbourn
Mathematics Subject Classification ID: 05B30
Mathematics Subject Classification ID: 20N05
zbMATH DE Number: 840229
zbMATH Keywords: cycle system
zbMATH Keywords: cycle decomposition
zbMATH Keywords: quasigroup
zbMATH Keywords: 2-perfect \(m\)-cycle systems
author: Darryn Bryant
author: C. C. Lindner
MaRDI profile type: Publication
cites work: Q4033704
cites work: Varieties of quasigroups arising from 2-perfect \(m\)-cycle systems
cites work: Q3983102
cites work: Steiner pentagon systems
cites work: Q3981348
cites work: Concerning the number of mutually orthogonal latin squares
cites work: Decompositions of edge-colored complete graphs
full work available at URL: https://doi.org/10.1007/bf01190966
OpenAlex ID: W1499434560
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description: scientific article; zbMATH DE number 840229