Transitive groups on the line at infinity of a finite affine plane

摘要

Collineation groups of finite projective planes and their geometries have been studied systemati cally since the beginning of the twentieth century. Special attention is devoted to collineation groups C of a finite projective plane Π which fix a line e and act on it with some transitivity properties. The main difficulty in dealing with this problem is the concurrent presence of Baer involutions and involutory perspectivities with axis e of the projective plane Π in the group C. Actually, the existence of involutory elations of axis e forces Π to be a translation plane and the problem is easier to tackle, since the theory of finite translation planes is extremely advanced. The case when G is 2-transitive on e has been completely solved over the years mainly by Cofman [6], Schulz [28] and Czerwinski [8,9], Kallaher [16], Korchmaros [19], and more recently by Biliotti and Francot [2].