EMIS ELibM Electronic Journals Publications de l'Institut Mathématique, Nouvelle Série
Vol. 81(95), pp. 111–117 (2007)

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Constructions of $(2,n)$-varieties of groupoids for $n=7,8,9$

Lidija Goracinova-Ilieva, Smile Markovski

University "Goce Delcev"-Stip, "Ss Cyril and Methodius"-Skopje

Abstract: Given positive integer $n>2$, an algebra is said to be a $(2,n)$-algebra if any of its subalgebras generated by two distinct elements has $n$ elements. A variety is called a $(2,n)$-variety if every algebra in that variety is a $(2,n)$-algebra. There are known only $(2,3)$-, $(2,4)$- and $(2,5)$-varieties of groupoids, and there is no $(2,6)$-variety. We present here $(2,n)$-varieties of groupoids for $n=7,8,9$.

Classification (MSC2000): 03C05; 20N05

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