Paramedial quasigroups of prime and prime square order

Abstract

We prove that, for every odd prime number p, there are 2p - 1 paramedial quasigroups of order p and 6p(2) - p - 1 paramedial quasigroups of order p(2), up to isomorphism. We present a complete list of those which are simple.

Keywords

• Paramedial quasigroups
• affine quasigroups
• enumeration of quasigroups
• simple quasigroups