Diagram geometries for sharply n-transitive sets of permutations or of mappings

A characterization of sharply n-transitive sets of permutations or of mappings is given by means of Buekenhout diagrams. As a by-product, a characterization is obtained in the same style for finite Minkowski and Laguerre planes. Two preliminary results are used to obtain these diagram-theoretic descriptions. One of them gives us a characterization of the complement of a square lattice graph by means of the nonexistence of certain configurations. The other one states that every net of degree s + 1 with s + 2 points on each line is embeddable in a projective plane of order s + 2. This latter result is exploited to get control over the geometries appearing as rank 2 residues on top in the diagrams we consider. Next, we can use the earlier result to obtain the information we need on the point-graphs of the geometries we want to describe. © 1992 Kluwer Academic Publishers.