A note on varieties of groupoids arising from \(m\)-cycle systems
type: Item
instance of: scholarly article
title: A note on varieties of groupoids arising from \(m\)-cycle systems
zbMATH Open document ID: 0827.05033
DOI: 10.1023/A:1022423910787
published in: Journal of Algebraic Combinatorics
publication date: 1995-11-27T00:00:00Z
review text: An \(m\)-cycle system is a decomposition of the complete graph \(K_n\) into disjoint cycles of length \(m\). Given a cycle system, we can define a binary operation on the vertex set of \(K_n\) and obtain a groupoid. If for a stated \(m\), the groupoids corresponding to all finite \(m\)-cycle systems are the finite members of a variety then we say that \(m\)-cycle systems are equationally defined. The author shows that the only values of \(m\) for which \(m\)-cycles systems can be equationally defined are 3 and 5.
reviewed by: Norman F. Quimpo
Mathematics Subject Classification ID: 05C38
Mathematics Subject Classification ID: 20N02
Mathematics Subject Classification ID: 08B05
Mathematics Subject Classification ID: 05C70
Mathematics Subject Classification ID: 05C25
zbMATH DE Number: 773834
zbMATH Keywords: \(m\)-cycle system
zbMATH Keywords: decomposition
zbMATH Keywords: groupoid
zbMATH Keywords: variety
zbMATH Keywords: equationally defined
author: Darryn Bryant
MaRDI profile type: Publication
cites work: \(2\)-perfect \(m\)-cycle systems can be equationally defined for \(m=3\), \(5\), and \(7\) only
cites work: Q3934450
cites work: Neighbor designs
cites work: Q4401969
cites work: Q4026150
cites work: Q3812270
cites work: Decompositions of edge-colored complete graphs
full work available at URL: a:1022423910787
OpenAlex ID: W185263983
description: scientific article; zbMATH DE number 773834