2017/08/27 by R. A. R. Monzo, Monzo, Robert A. R., Wiesław A. Dudek +1
Engineering · Mathematics · #20M02 #20M15 #Advanced Mathematical Theories #FOS: Mathematics #Mathematics and Applications #Rings and Algebras (math.RA) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1708.08830
openalex publication_date 2017/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The concept of a k-translatable groupoid is introduced. Those k-translatable quadratical quasigroups induced by the additive group of integers modulo m, where k<40, are listed for m<1200. The fine structure of quadratical quasigroups is explored in detail and the Cayley tables of quadratical quasigroups of orders 5, 9, 13 and 17 are produced. All but those of order 9 are k-translatable, for some k. Open questions and thoughts about future research in this area are given.