School of Mathematical Sciences

Symmetries of generalised polygons menu

Symmetries of generalised polygons

Tomasz Popiel (QMUL)
Mon, 28/11/2016 - 16:30
FB 3.11
Seminar series: 

Generalised polygons are point?line incidence geometries introduced by Jacques Tits in an attempt to find geometric models for finite simple
groups of Lie type. A famous theorem of Feit and G. Higman asserts that the only "non-trivial"examples are generalised triangles (projective
planes), quadrangles, hexagons and octagons. In each case, there are "classical" examples associated with certain Lie type groups, and in the
latter two cases these are the only known examples. The classical examples are highly symmetric; in particular, their automorphism groups act
transitively on flags and primitively on both points and lines. There have been various attempts to classify generalised polygons subject to
symmetry assumptions whether weaker, stronger, or just different to those mentioned above and perhaps one of the strongest results in this
direction is a theorem of Kantor from 1987, asserting that a point-primitive projective plane is either classical (Desarguesian) or has a
prime number of points and a severely restricted automorphism group. I will review some on-going work with John Bamberg, Stephen Glasby, Luke
Morgan, Cheryl Praeger and Csaba Schneider that aims to classify the point-primitive generalised quadrangles, hexagons and octagons.