Varieties of quasigroups arising from 2-perfect \(m\)-cycle systems
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 \(m\).
scientific article; zbMATH DE number 95054