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Tim Burness (Bristol)
Wednesday 07 March 2018, 16:30-17:30
The Saxl graph of a permutation group
- đ¤ Speaker: Tim Burness (Bristol)
- đ Date & Time: Wednesday 07 March 2018, 16:30 - 17:30
- đ Venue: MR12
Abstract
Let G be a permutation group on a set X and recall that a subset of X is a base for G if its pointwise stabiliser is trivial. If G has a base of size 2, then we can associate a graph to G, with vertex set X and two points joined by an edge if they form a base. We call this the Saxl graph of G. In this talk I will start with a brief introduction to bases, focussing on primitive groups and probabilistic methods for bounding the minimal size of a base. I will then introduce the Saxl graph and present some of its basic properties (mainly in the context of a finite transitive group). I will finish by discussing some recent results and open problems. This is joint work with Michael Giudici.
Series This talk is part of the Algebra and Representation Theory Seminar series.
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