Varieties of Hexagonal Quasigroups
نویسندگان
چکیده
منابع مشابه
Symmetries in Hexagonal Quasigroups
When it doesn’t cause confusion, we can omit the sign “·”, e.g. instead of (a · b) · (c · d) we may write ab · cd. In this article, Q will always be a hexagonal quasigroup. The basic example of hexagonal quasigroup is formed by the points of Euclidean plane, with the operation · such that the points a, b and a · b form a positively oriented regular triangle. This structure was used for all the ...
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Decompositions of complete undirected graphs into sets of closed trails which partition the edge set of the graph and which contain each pair of distinct vertices exactly once at distance 2 define and are defined by a class of quasigroups called P-quasigroups. Conditions are established under which P-quasigroups are (or are not) homomorphic images of P-quasigroups which possess certain properti...
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A quasigroup identity is of Bol-Moufang type if two of its three variables occur once on each side, the third variable occurs twice on each side, the order in which the variables appear on both sides is the same, and the only binary operation used is the multiplication, viz. ((xy)x)z = x(y(xz)). Many well-known varieties of quasigroups are of Bol-Moufang type. We show that there are exactly 26 ...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1993
ISSN: 0021-8693
DOI: 10.1006/jabr.1993.1179