Geodesic
Constructions of (2,n)-varieties of groupoids for n = 7, 8, 9
Publications de l'Institut Mathématique, _N_S_81 (2007) no. 95, p. 111 .

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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 $n=7,8,9$.
DOI : 10.2298/PIM0795111G
Classification : 03C05 20N05
Keywords: (2,n)-algebra, quasigroup, variety 
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     title = {Constructions of (2,n)-varieties of groupoids for n = 7, 8, 9},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {111 },
     publisher = {mathdoc},
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     year = {2007},
     doi = {10.2298/PIM0795111G},
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Lidija Goraèinova-Ilieva; Smile Markovski. Constructions of (2,n)-varieties of groupoids for n = 7, 8, 9. Publications de l'Institut Mathématique, _N_S_81 (2007) no. 95, p. 111 . doi : 10.2298/PIM0795111G. http://geodesic.mathdoc.fr/articles/10.2298/PIM0795111G/

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