Maximally nonassociative quasigroups via quadratic orthomorphisms

Abstrakt

A quasigroup Q is called maximally nonassociative if for x, y, z ELEMENT OF 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 6 p2 < 2p1.

Klíčová slova

• Maximally
• nonassociative
• quasigroups
• via
• quadratic
• orthomorphisms