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Bases for permutation groups

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  • UserHongyi Huang (Bristol)
  • ClockThursday 30 November 2023, 15:00-16:00
  • HouseLG06 Old Gym.

If you have a question about this talk, please contact Chris Parker.

Let $G\leqslant\mathrm{Sym}(\Omega)$ be a permutation group on a finite set $\Omega$. A base for $G$ is a subset of $\Omega$ with trivial pointwise stabiliser, and the base size of $G$, denoted $b(G)$, is the minimal size of a base for $G$. This classical concept has been studied since the early years of permutation group theory in the nineteenth century, finding a wide range of applications.

Recall that $G$ is called primitive if it is transitive and its point stabiliser is a maximal subgroup. Primitive groups can be viewed as the basic building blocks of all finite permutation groups, and much work has been done in recent years in bounding or determining the base sizes of primitive groups. In this talk, I will report on recent progress of this study. In particular, I will give the first family of primitive groups arising in the O’Nan-Scott theorem for which the exact base size has been computed in all cases.

This talk is part of the Algebra seminar series.

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