1. Introduction In this paper we consider some results on the orbits of groups of collineations, or, more generally, on the point and block classes of tactical decompositions, on symmetric balanced incomplete block designs (symmetric BIBD = (v, k, 2)-system=finite 2-plane), and we consider generalizations to (not necessarily symmetric) BIBD and other combinatorial designs. The results are about...

In this paper we characterize the automorphisms (collineations) of the Segre product of partial linear spaces. In particular, we show that if all components of the product are strongly connected, then every collineation is determined by a set of isomorphisms between its components. The formalization follows the ideas presented in the Journal of Geometry paper [16] by Naumowicz and Prażmowski.

We consider point-line geometries having three points on every line, having three lines through every point (bislim geometries), and containing triangles. We classify such geometries under the hypothesis of the existence of a collineation group acting transitively on the point set.

Connections are made between deficiency one α-flokki and Baer groups of associated α-flokki translation planes, extending the theory of Johnson and Payne-Thas. The full collineation group of an α-flokki is completely determined. Many of the ideas are extended to the infinite case.