Finite Doubly Transitive Affine Planes

On Finite Point Transitive Affine Planes with Two Orbits

Finite flag-transitive affine planes with a solvable automorphism group

In this paper, we consider finite flag-transitive affine planes with a solvable automorphism group. Under a mild number-theoretic condition involving the order and dimension of the plane, the translation complement must contain a linear cyclic subgroup that either is transitive or has two equal-sized orbits on the line at infinity. We develop a new approach to the study of such planes by associ...

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.

Two Families of Flag-transitive Affine Planes

Two families of flag-transitive nondesarguesian affine planes of odd order are defined, and isomorphisms among the various planes are studied. Thir ty years ago Wagner [5] proved the impor tan t result that every finite flag-transitive affine plane is a t ranslat ion plane. However , since that t ime relatively few classes of such planes have been found. The purpose of this note is to c o m m e...

Flag-transitive Extensions of Dual Affine Planes

(with 1 , q , ̀ ) . An infinite family of simply connected examples for this diagram with q 5 2 is obtained by truncating Coxeter complexes of type D n . Two dif ferent finite families with three members and q 5 4 arise from the Steiner systems for the Mathieu groups M 2 2 , M 2 3 and M 2 4 . The geometries of these two families are simply connected . Three more simply connected examples of rank...