Maximal nonassociativity via fields

Petr Lisonek

We say that $(x,y,z)\in Q^3$ is an associative triple in a quasigroup $Q(\ast )$ if $(x\ast y)\ast z=x\ast (y\ast z)$. Let $a(Q)$ denote the number of associative triples in $Q$. It is easy to show th…