English

Translatable quadratical quasigroups

Rings and Algebras 2017-08-30 v1

Abstract

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.

Keywords

Cite

@article{arxiv.1708.08830,
  title  = {Translatable quadratical quasigroups},
  author = {Robert A. R. Monzo and Wieslaw A. Dudek},
  journal= {arXiv preprint arXiv:1708.08830},
  year   = {2017}
}

Comments

25 pages, 7 Cayley tables and 9 other tables. arXiv admin note: text overlap with arXiv:1603.08502

R2 v1 2026-06-22T21:26:45.141Z