SEMINAR: Groups and Combinatorics Seminar: Affine rank 3 partial linear spaces

Time and place: 15:00 Friday 14 August in Blakers LT.

Speaker: Joanna Fawcett (University of Western Australia)

Title: Affine rank 3 partial linear spaces

Abstract: A partial linear space consists of a finite non-empty set P of points and a collection L of subsets of P called lines such that every pair of points lies on at most one line, and every line contains at least two points. A partial linear space is proper if it is not a graph (i.e., every line contains exactly two points) or a linear space (i.e., every pair of points lies on exactly one line). Proper partial linear spaces with the most symmetry are those for which the automorphism group acts transitively on pairs of collinear points and pairs of non-collinear points. Such a geometry admits a transitive rank 3 group of automorphisms, and when this group is primitive, it is of almost simple, grid or affine type. Devillers classified the proper partial linear spaces admitting a primitive rank 3 group of automorphisms of almost simple or grid type. In this talk, we will consider some recent progress on the affine case. This is joint work with Bamberg, Devillers and Praeger.