TRANSLATION PLANES OF ODD ORDER VIA DEMBOWSKI–OSTROM POLYNOMIALS

We describe a class of translation planes whose orders are of the form q n , where n is odd and q is an odd prime power 3. These planes have the property that a translation complement fixes a triangle and acts transitive ly on the set of non-vertices of each side. The planes form an odd order analogue to the planes of Kantor‐ Williams [17] which have even order. The construction of the planes is based on a certain type of Dembowski‐Ostrom polynomials.