A note on varieties of groupoids arising from \(m\)-cycle systems
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.
scientific article; zbMATH DE number 773834