A class of generalized quadrangles and their automorphism group.
Stefaan De Winter
University of Ghent

Abstract:

I will start by defining generalized quadrangles (GQ) and discussing some elementary properties of these geometries. Then Stanley Payne's construction of a GQ P of order (s-1,s+1) out of a GQ Q of order (s,s) with a regular point will be explained. The determination of the automorphism group of this so-called Payne-derived GQ is a longstanding open problem. The conjecture is that for odd s this group should be the group naturally induced on P by the automorphism group of Q (it is known that this is not true for even s). In a joint work with K. Thas we proved this conjecture to be true if the regular point of Q is a so-called center of symmetry. The proof uses purely geometrical, combinatorial and some unexpected group theoretical arguments.