Endomorphisms of abelian group isotope semisymmetrizations [Articol]

Abstract

Semisymmetrization and Mendelsohnization allow quasigroup homotopies to be reduced to homomorphisms. We demonstrate the semisymmetrization of an abelian group isotope is isomorphic to the direct product of its Mendelsohnization and another specific isotope if and only if its order is not divisible by 3. We also provide an example of a quasigroup such that the idempotent replica of its semisymmetrization is trivial.