, Volume 70, Issue 4, pp 349-357
Date: 23 Jun 2003

On the Existence of Totally Anti-Symmetric Quasigroups of Order 4k +2

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


Totally anti-symmetric quasigroups are employed in check digit systems. We give counterexamples to a conjecture of Ecker and Poch and show that there are totally anti-symmetric quasigroups for all orders n≡0,1,34, n=4(5k+2)+2, and n=4(7k+3)+2. We prove that finite totally anti-symmetric quasigroups possess a transversal, and we give a useful condition for quasigroups not to have a transversal.