Maximally nonassociative quasigroups via quadratic orthomorphisms
Algebraic Combinatorics, Volume 4 (2021) no. 3, pp. 501-515.

A quasigroup Q is called maximally nonassociative if for x,y,zQ 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: https://doi.org/10.5802/alco.165
Classification: 20N05,  11T22,  05D99,  05E16
Keywords: Quasigroup, maximally nonassociative, quadratic orthomorphism, idempotent.
@article{ALCO_2021__4_3_501_0,
     author = {Dr\'apal, Ale\v{s} and Wanless, Ian M.},
     title = {Maximally nonassociative quasigroups via quadratic orthomorphisms},
     journal = {Algebraic Combinatorics},
     pages = {501--515},
     publisher = {MathOA foundation},
     volume = {4},
     number = {3},
     year = {2021},
     doi = {10.5802/alco.165},
     language = {en},
     url = {https://alco.centre-mersenne.org/articles/10.5802/alco.165/}
}
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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