Abstract:
We enumerate central and medial quasigroups of order less than $128$ up to isomorphism, with the exception of those quasigroups that are isotopic to $C_4\times C_2^4$, $C_2^6$, $C_3^4$ or $C_5^3$. We give an explicit formula for the number of quasigroups that are affine over a finite cyclic group.
Keywords and phrases:medial quasigroup, entropic quasigroup, central quasigroup, $\mathrm T$-quasigroup, abelian quasigroup, quasigroup affine over abelian group, abelian algebra, affine algebra, classification of quasigroups, enumeration of quasigroups.
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