A Remark on Benz Planes of Order \(9\)

Giinter F.Steinke1
1 Department of Mathematics and Statistics University of Auckland Private Bag Auckland, NEW ZEALAND

Abstract

Using the explicit determination of all ovals in the 3 non-Desarguesian projective planes of order 9 given in [4] or [8], we prove that there are no other Benz planes of order 9 than the three miquelian planes and the Minkowski plane over the Dickson near-field of type \(\{3,2\}\).