Geodesic
Quasigroup covers of division groupoids
Commentationes Mathematicae Universitatis Carolinae, Tome 64 (2023) no. 3, pp. 265-278.

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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.
DOI : 10.14712/1213-7243.2024.002
Classification : 20N05
Keywords: groupoid; division; quasigroup; cover 
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Ježek, Jaroslav J.; Kepka, Tomáš J.; Němec, Petr C. Quasigroup covers of division groupoids. Commentationes Mathematicae Universitatis Carolinae, Tome 64 (2023) no. 3, pp. 265-278. doi : 10.14712/1213-7243.2024.002. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2024.002/

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