Two-transitive orbits in finite projective planes (Q2573747)

This paper contains partly a survey, partly new results on the following question. Given a collineation group of a finite affine or projective plane of order \(n\) with an orbit of size at least \(n\) on which the group acts two-transitively, what can we say about the plane and the orbit? Many results are mentioned and proved in the paper under review. Essentially, there are three cases: the orbit either is contained in a line, or is a \(k\)-arc (\(k\in\{n,n+1,n+2\}\)), or the lines of the plane induce a nontrivial 2-design. In the latter case, there is a classification due to Kantor, and so one has to study the embedding problem of such designs. In the first two cases, not everything is settled yet, but the authors improve a lot of known results.