Maximal nonassociativity via nearfields

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10420774" target="_blank" >RIV/00216208:11320/20:10420774 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=u9F56sNiy_" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=u9F56sNiy_</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.ffa.2019.101610" target="_blank" >10.1016/j.ffa.2019.101610</a>

Result language
angličtina
Original language name
Maximal nonassociativity via nearfields
Original language description
We say that (x, y, z) Q3 is an associative triple in a quasigroup Q(*) if (x * y) * z = x * (y * z). It is easy to show that the number of associative triples in Q is at least (Q), and it was conjectured that quasigroups with exactly (Q) associative triples do not exist when (Q) >1. We refute this conjecture by proving the existence of quasigroups with exactly (Q) associative triples for a wide range of values (Q). Our main tools are quadratic Dickson nearfields and the Weil bound on quadratic character sums.
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
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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