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arXiv · 1912.07040

Maximally nonassociative quasigroups via quadratic orthomorphisms

Ales Drapal·Ian M. Wanless
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Abstract

A quasigroup $Q$ is called maximally nonassociative if for $x,y,z\in Q$ we have that $x\cdot (y\cdot z) = (x\cdot y)\cdot z$ 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 $n=2p_1p_2$ for primes $p_1,p_2$ with $p_1\le p_2<2p_1$.

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Ales Drapal, Ian M. Wanless. 2020-12-16. Maximally nonassociative quasigroups via quadratic orthomorphisms. https://doi.org/10.5802/alco.165

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