Semisymmetrization and Mendelsohn quasigroups

The semisymmetrization of an arbitrary quasigroup builds a semisymmetric structure on the cube underlying set quasigroup. It serves to reduce homotopies homomorphisms. An alternative square was recently introduced by A. Krapež and Z. Petrić. Their construction in fact yields Mendelsohn quasigroup, which is idempotent as well semisymmetric. We describe it Mendelsohnization original For quasigroups isotopic abelian group, relation between studied. shown that total space for action group. group isotope then identified replica its semisymmetrization, with fibers isomorphic