SEMINAR: Groups and Combinatorics Seminar, Antiflag-transitive generalized quadrangles

Eric Swartz (UWA)

will speak on

Antiflag-transitive generalized quadrangles

at 3pm Friday 14 November in Mathematics Lecture Room 1.

Abstract:

A generalized quadrangle is a point-line incidence geometry Q such that (1) any two points lie on at most one line, and (2) given a line l and a point P not incident with l, P is collinear with a unique point of l. An antiflag of a generalized quadrangle is a non-incident point-line pair (P, l), and we say that the generalized quadrangle Q is antiflag-transitive if the group of collineations (automorphisms that send points to points and lines to lines) is transitive on the set of all antiflags. We prove that if a finite, thick generalized quadrangle Q is antiflag-transitive, then Q is one of the following: the unique generalized quadrangle of order (3,5), a classical generalized quadrangle, or a dual of one of these. This is joint work with John Bamberg and Cai-Heng Li.