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Construction of Mendelsohn designs by using quasigroups of ( 2 , q ) -varieties

Lidija Goračinova-Ilieva;  Smile Markovski — 2016

Commentationes Mathematicae Universitatis Carolinae

Let q be a positive integer. An algebra is said to have the property ( 2 , q ) if all of its subalgebras generated by two distinct elements have exactly q elements. A variety 𝒱 of algebras is a variety with the property ( 2 , q ) if every member of 𝒱 has the property ( 2 , q ) . Such varieties exist only in the case of q prime power. By taking the universes of the subalgebras of any finite algebra of a variety with the property ( 2 , q ) , 2 < q , blocks of Steiner system of type ( 2 , q ) are obtained. The stated correspondence between Steiner...

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