The Saxl graph of a permutation group

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• Tim Burness (Bristol)
• Wednesday 07 March 2018, 16:30-17:30
• MR12.

If you have a question about this talk, please contact Eugenio Giannelli.

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.

This talk is part of the Algebra and Representation Theory Seminar series.

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