Growth in groups and CFSG-free proofs

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• Laszlo Pyber (Alfréd Rényi Institute of Mathematics,Hungarian Academy of Sciences)
• Thursday 30 June 2022, 16:00-17:00
• Seminar Room 1, Newton Institute.

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GRA2 - Groups, representations and applications: new perspectives

The proof of the Product Theorem of Breuillard-Green-Tao and Pyber-Szabo is closely related to the CFSG -free proof of Weisfeiler’s theorem on linear groups of bounded rank, due to Larsen-Pink. Ideas from CFSG -free proofs have also been used to obtain results about growth in unbounded rank situations. Somewhat surprisingly we show that, on the other hand, the deep (but CFSG -free) theorem of Breuillard-Green-Tao on non-growing subsets of  arbitrary groups can be used to obtain bounds on the orders of primitive permutation groups.  This is joint work with Sean Eberhard.

This talk is part of the Isaac Newton Institute Seminar Series series.

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