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Extremely primitive groups

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Let G be a finite primitive permutation group acting on a set X with nontrivial point stabiliser G_x. We say that G is extremely primitive if G_x acts primitively on every orbit in X \ {x}. These groups arise naturally in several different contexts and their study can be traced back to work of Manning in the 1920s. After surveying previous results we will discuss recent joint work with Tim Burness completing this classification. Most of the work is in dealing with almost simple groups with socle an exceptional group of Lie type. We will describe the various techniques used in the proof and in particular, discuss the results we proved on bases for primitive actions of exceptional groups.

This talk is part of the Algebra seminar series.

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