Flag-transitive planes of even order

New Flag-Transitive Affine Planes of Even Order

At least [6 n&1 1 (q i+1)] qn 2m1 log2 q of these planes have kernel GF(q). Moreover, we construct 7(mi)6i q mi planes, where the sum is over all sequences (mi) behaving as in the theorem; and then we settle the isomorphism problem for these planes (Theorem 5.2). The proof combines methods in [Wi] and [Ka]: these planes arise from symplectic and orthogonal spreads combined with changing from fi...

Cubic Extensions of Flag-transitive Planes, I. Even Order

The collineation groups of even order translation planes which are cubic extensions of flag-transitive planes are determined. 2000 Mathematics Subject Classification. Primary 51E.

Flag-transitive Planes of Even Order1

Transitive Arcs in Planes of Even Order

When one considers the hyperovals in PG (2 , q ) , q even , q . 2 , then the hyperoval in PG (2 , 4) and the Lunelli – Sce hyperoval in PG (2 , 16) are the only hyperovals stabilized by a transitive projective group [10] . In both cases , this group is an irreducible group fixing no triangle in the plane of the hyperoval , nor in a cubic extension of that plane . Using Hartley’s classification ...

Nearly flag-transitive affine planes

Spreads of orthogonal vector spaces are used to construct many translation planes of even order q, for odd m > 1, having a collineation with a (q − 1)-cycle on the line at infinity and on each of two affine lines.