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Maximally nonassociative quasigroups via quadratic orthomorphisms
Drápal, Aleš1; Wanless, Ian M.2
1 Department of Mathematics Charles University Sokolovská 83 186 75 Praha 8, Czech Republic
2 School of Mathematics Monash University Clayton Vic 3800, Australia
Algebraic Combinatorics, Volume 4 (2021) no. 3, pp. 501-515.

A quasigroup Q is called maximally nonassociative if for x,y,z∈Q we have that x·(y·z)=(x·y)·z only if x=y=z. We show that, with finitely many exceptions, there exists a maximally nonassociative quasigroup of order n whenever n is not of the form n=2p 1 or n=2p 1 p 2 for primes p 1 ,p 2 with p 1 ≤p 2 <2p 1 .

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DOI: 10.5802/alco.165
Classification: 20N05, 11T22, 05D99, 05E16
Keywords: Quasigroup, maximally nonassociative, quadratic orthomorphism, idempotent.

Drápal, Aleš 1; Wanless, Ian M. 2

1 Department of Mathematics Charles University Sokolovská 83 186 75 Praha 8, Czech Republic
2 School of Mathematics Monash University Clayton Vic 3800, Australia
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Drápal, Aleš; Wanless, Ian M. Maximally nonassociative quasigroups via quadratic orthomorphisms. Algebraic Combinatorics, Volume 4 (2021) no. 3, pp. 501-515. doi : 10.5802/alco.165. https://alco.centre-mersenne.org/articles/10.5802/alco.165/

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