Varieties of quasigroups arising from 2-perfect \(m\)-cycle systems
type: Item
instance of: scholarly article
title: Varieties of quasigroups arising from 2-perfect \(m\)-cycle systems
zbMATH Open document ID: 0767.05065
DOI: 10.1007/BF00124894
author: Darryn Bryant
published in: Designs, Codes and Cryptography
publication date: 1993-01-16T00:00:00Z
review text: Let \((K_ r,C)\) be a decomposition of the complete graph \(K_ r\) into \(m\)-cycles \(C\) such that every pair of vertices occurs at distance 2 in exactly one cycle of \(C\). Let \(a*a=a\) and \(a*b=c\), where the edge \(ab\) is adjacent to the edge \(bc\) in a cycle of \(C\). It is shown that the class of quasigroups, arising from all \(m\)-cycle systems does not form a variety for most \(m\).
Mathematics Subject Classification ID: 05C70
Mathematics Subject Classification ID: 20N05
Mathematics Subject Classification ID: 05C38
Mathematics Subject Classification ID: 05B15
zbMATH DE Number: 95054
zbMATH Keywords: decomposition
zbMATH Keywords: complete graph
zbMATH Keywords: \(m\)-cycle systems
reviewed by: Victor Ufnarovski
MaRDI profile type: Publication
cites work: Q3097395
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cites work: 2-perfect \(m\)-cycle systems
cites work: Steiner pentagon systems
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full work available at URL: https://doi.org/10.1007/bf00124894
OpenAlex ID: W1969446947
description: scientific article; zbMATH DE number 95054