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Medial quasigroups of prime square order

David Stanovský (2016)

Commentationes Mathematicae Universitatis Carolinae

We prove that, for any prime p , there are precisely 2 p 4 - p 3 - p 2 - 3 p - 1 medial quasigroups of order p 2 , up to isomorphism.

Medial quasigroups of type ( n , k )

Alena Vanžurová (2010)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Our aim is to demonstrate how the apparatus of groupoid terms (on two variables) might be employed for studying properties of parallelism in the so called ( n , k ) -quasigroups. We show that an incidence structure associated with a medial quasigroup of type ( n , k ) , n > k 3 , is either an affine space of dimension at least three, or a desarguesian plane. Conversely, if we start either with an affine space of order k > 2 and dimension m , or with a desarguesian affine plane of order k > 2 then there is a medial quasigroup of...

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