SEMINAR: Groups and Combinatorics Seminar: Point-primitive, line-transitive generalised quadrangles of 'holomorph type'

Time and place: 15:00 Friday 25 September in Blakers LT.

Speaker: Tomasz Popiel (University of Western Australia)

Title: Point-primitive, line-transitive generalised quadrangles of 'holomorph type'.

Abstract: In a 2012 paper, Bamberg, Giudici, Morris, Royle and Spiga showed that a group acting primitively on both the points and the lines of a (finite and thick) generalised quadrangle must be an almost simple group of Lie type. In on-going work, we seek to weaken their assumption to primitivity on points and transitivity on lines, and classify the resulting examples. This has proved extremely difficult. In joint work with Bamberg, Glasby and Praeger, we have classified the examples for which the primitive action on points is of affine type. In joint work with Bamberg and Praeger, we have now also shown that no examples arise when the primitive action on points is of holomorph simple or holomorph compound type. In this highly anticipated talk, I will give some ideas of the proof of the latter result.