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Quasigroup covers of division groupoids

Jaroslav J. Ježek; Tomáš Kepka; Petr Němec — 2023

Commentationes Mathematicae Universitatis Carolinae

Let $G$ be a division groupoid that is not a quasigroup. For each regular cardinal $α > | G |$ we construct a quasigroup $Q$ on $G \times α$ 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.

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