Finite p-groups, Kantor systems, and generalized quadrangles

Generalized quadrangles play an important role in several areas of mathematics, such as in algebra and in geometry. Kantor in the 80's showed that an important class of generalized quadrangles can be constructed from certain sets of subgroups in finite groups. These sets are now called Kantor systems. In this talk, I will explain the connection between generalized quadrangles, finite groups, and Kantor systems and will characterize Kantor systems in groups of order p^5. The new results presented in this lecture were obtained in collaboration with John Bamberg (Ghent) and Tim Penttila (Colorado).