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Drápal, Aleš; Griggs, Terry S. and Kozlik, Andrew R.
(2022).
DOI: https://doi.org/10.1142/s0218196722500308
Abstract
Let the product of points A and B be the vertex C of the right isosceles triangle for which AB is the base, and ABC is oriented anticlockwise. This yields a quasigroup that satisfies laws (xu) (vy) = (xv)(uy), (xy)(yx) = y and xx = x. Such quasigroups are called quadratical. Quasigroups that satisfy only the latter two laws are equivalent to perfect Mendelsohn designs of length four (PMD(v,4)). This paper examines various algebraic identities induced by PMD(v,4), classifies finite quadratical quasigroups, and shows how the square structure of quadratical quasigroups is associated with toroidal grids.
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About
- Item ORO ID
- 82222
- Item Type
- Journal Item
- ISSN
- 1793-6500
- Keywords
- Perfect Mendelsohn design; quadratical quasigroup; third Stein’s law; toroidal grid; second Schröder’s law
- Academic Unit or School
-
Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
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