Abstract: Let G be a division groupoid that is not a quasigroup. For each regular cardinal \alpha>|G| we construct a quasigroup Q on G\times\alpha that is a quasigroup cover of G (i.e., G is a homomorphic image of Q and G is not an image of any quasigroup that is a proper factor of Q). We also show how to easily obtain quasigroup covers from free quasigroups.
Keywords: groupoid; division; quasigroup; cover
DOI: DOI 10.14712/1213-7243.2024.002
AMS Subject Classification: 20N05