Flokki planes and cubic polynomials


Non-Desarguesian translation planes of order q^2 are constructed whenever q=2^e\ge 16 and e isnot divisible by 3. Each plane has kernel \textnormal{GF}(q)  andtranslation complement of order q(q-1)^2 e, with orbits of lengths1, q and q^2-q on the translation line. The planes have elation groups oforder q that producederivable nets, but are not flock planes, semifield planes,  orlifted planes.
The same algebraic tools are used to construct  non-Desarguesiantranslation planes of order2^p for every prime p>3.

DOI Code: 10.1285/i15900932v29n1supplp211

translation planes

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