Flokki planes and cubic polynomials

Abstract

Non-Desarguesian translation planes of order are constructed whenever and isnot divisible by . Each plane has kernel andtranslation complement of order , with orbits of lengths and on the translation line. The planes have elation groups oforder that producederivable nets, but are not flock planes, semifield planes, orlifted planes. The same algebraic tools are used to construct non-Desarguesiantranslation planes of order for every prime .