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Bases for primitive permutation groups

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Let $G \leq \mathrm{Sym}(\Omega)$ be a primitive permutation group. A base for $G$ is a subset $B \subseteq \Omega$ such that the pointwise stabiliser $G_B=1$. In this talk, after outlining the history and uses of bases, I will describe some recent work towards two prominent problems in the area – namely the solution to Pyber’s conjecture and the classification of primitive groups with base size two.

This talk is part of the Algebra Seminar series.

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