ISOMORPHISMS OF QUADRATIC QUASIGROUPS

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10472324" target="_blank" >RIV/00216208:11320/23:10472324 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=lm9JsOK6mW" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=lm9JsOK6mW</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1017/S0013091523000585" target="_blank" >10.1017/S0013091523000585</a>

Result language
angličtina
Original language name
ISOMORPHISMS OF QUADRATIC QUASIGROUPS
Original language description
Abstract Let F be a finite field of odd order and a, b ELEMENT OF F {0, 1} be such that χ(a) = χ(b) and χ(1 - a) = χ(1 - b), where χ is the extended quadratic character on F. Let Qa,b be the quasigroup over F defined by (x, y) 7RIGHTWARDS ARROW x + a(y - x) if χ(y - x) > 0, and (x, y) 7RIGHTWARDS ARROW x + b(y - x) if χ(y - x) = -1. We show that Qa,b TILDE OPERATOR+D91= Qc,d if and only if {a, b} = {α(c), α(d)} for some α ELEMENT OF Aut(F). We also characterize Aut(Qa,b) and exhibit further properties, including establishing when Qa,b is a Steiner quasigroup or is commutative, entropic, left or right distributive, flexible or semisymmetric. In proving our results, we also characterize the minimal subquasigroups of Qa,b.
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
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/LTAUSA19070" target="_blank" >LTAUSA19070: Commutators, quasigroups and Yang Baxter equation</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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