Units in generalized derivatives of quasigroups

Abstract

We proceed the research of generalized quasigroup derivatives started in early papers of the last co-author ([20, p. 212], [13]). For any quasigroup there exist 648 generalized derivatives. Here we study the problem about existence of units (left, right, middle) in quasigroups that are a generalized derivative of a quasigroup. There exist 1944 various cases. For every case we find a proof or a counterexample, often using Prover or Mace [15, 14].