群与图讨论班 Seminars on Groups and Graphs

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Regular orbits of primitive groups on power sets

黄弘毅 Hong Yi Huang

University of Bristol

Time: 16:00-18:00 (GMT+8), Saturday February 19th, 2022
Location: Tencent Meeting

Abstract: In this talk, I will first review the famous O'Nan-Scott Theorem by discussing its several versions. As an application, I will classify the primitive groups $$G\leqslant\operatorname{Sym}(\Omega)$$ with unique regular orbit on the power set of $$\Omega$$, which is joint with Tim Burness and extends earlier results due to Seress and Dolfi. I will also introduce some interesting connections to a diverse range of group theory problems, including minimal degrees, base sizes and distinguishing numbers. Finally, we will see an application to the automorphism groups of $$2$$-arc-transitive graphs.

Host: 丁兆宸 Zhaochen Ding

Slides