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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...

On Semigroups Defined by the Identity xxy = y

Smile Markovski; Ana Sokolova; Lidija Goracinova Ilieva — 2001

Publications de l'Institut Mathématique

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

On Semigroups Defined by the Identity xxy = y

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