Quadratical quasigroups and Mendelsohn designs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10452392" target="_blank" >RIV/00216208:11320/22:10452392 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=fxx5zyO3a2" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=fxx5zyO3a2</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1142/S0218196722500308" target="_blank" >10.1142/S0218196722500308</a>

Result language
angličtina
Original language name
Quadratical quasigroups and Mendelsohn designs
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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