ON THE NUMBER OF QUADRATIC ORTHOMORPHISMS THAT PRODUCE MAXIMALLY NONASSOCIATIVE QUASIGROUPS

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10471873" target="_blank" >RIV/00216208:11320/23:10471873 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=KL87B~feZE" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=KL87B~feZE</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1017/S1446788722000386" target="_blank" >10.1017/S1446788722000386</a>

Result language
angličtina
Original language name
ON THE NUMBER OF QUADRATIC ORTHOMORPHISMS THAT PRODUCE MAXIMALLY NONASSOCIATIVE QUASIGROUPS
Original language description
Let q be an odd prime power and suppose that a,bELEMENT OFFq are such that ab and (1-a)(1-b) are nonzero squares. Let Qa,b=(Fq,ASTERISK OPERATOR) be the quasigroup in which the operation is defined by uASTERISK OPERATORv=u+a(v-u) if v-u is a square, and uASTERISK OPERATORv=u+b(v-u) if v-u is a nonsquare. This quasigroup is called maximally nonassociative if it satisfies xASTERISK OPERATOR(yASTERISK OPERATORz)=(xASTERISK OPERATORy)ASTERISK OPERATORzLEFT RIGHT DOUBLE ARROWx=y=z. Denote by σ(q) the number of (a,b) for which Qa,b is maximally nonassociative. We show that there exist constants αALMOST EQUAL TO0.02908 and βALMOST EQUAL TO0.01259 such that if qIDENTICAL TO1mod4, then limσ(q)/q2=α, and if qIDENTICAL TO3mod4, then limσ(q)/q2=β.
Czech name
—
Czech description
—

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

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

Similar results(10)