Maximally nonassociative quasigroups via quadratic orthomorphisms

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 $n=2p_1{p}_2$ for primes $p_1,p_2$ with $p_1\le p_2<2p_1$.

References in corpus (1)

• On the number of quadratic orthomorphisms that produce maximally nonassociative quasigroups

Cited by in corpus (3)

• On the number of quadratic orthomorphisms that produce maximally nonassociative quasigroups
• Isomorphisms of quadratic quasigroups
• Cycles of quadratic Latin squares and anti-perfect $1$-factorisations