\(2\)-perfect \(m\)-cycle systems can be equationally defined for \(m=3\), \(5\), and \(7\) only (Q1906520)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: \(2\)-perfect \(m\)-cycle systems can be equationally defined for \(m=3\), \(5\), and \(7\) only |
scientific article; zbMATH DE number 840229
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(2\)-perfect \(m\)-cycle systems can be equationally defined for \(m=3\), \(5\), and \(7\) only |
scientific article; zbMATH DE number 840229 |
Statements
\(2\)-perfect \(m\)-cycle systems can be equationally defined for \(m=3\), \(5\), and \(7\) only (English)
0 references
25 February 1996
0 references
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.
0 references
cycle system
0 references
cycle decomposition
0 references
quasigroup
0 references
2-perfect \(m\)-cycle systems
0 references
0.95234853
0 references
0.9289368
0 references
0.89257634
0 references
0 references
0.84662306
0 references
0.8132626
0 references
