Maximally nonassociative quasigroups via quadratic orthomorphisms
A quasigroup Q is said to be maximally nonassociative if for
x,y,z in 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=2p1 or n=2p1p2 for primes p1,p2 with p1≤p2<2p1.