Abstrakt
The main concern of this paper are quasigroups of order nine that possess at most 18 associative triples. The order nine is the least order for which there exists a quasigroup (Q,*) such that x * (y * z)=(x * y) * z holds if and only if x=y=z.
Up to isomorphism there is only one such quasigroup of this order. It has remarkable properties that bind it to a nearfield, to a PMD (9,4) and to a Sudoku division square.