# 群与图讨论班 Seminars on Groups and Graphs

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# A classification of finite groups with three automorphism orbits

## 朱砚舟 Yanzhou Zhu

SUSTech

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

Abstract: Denote by $$\omega(G)$$ the number of orbits of the action of Aut$$(G)$$ on a finite group $$G$$. It is well-known that $$\omega(G)=2$$ if and only if $$G$$ is an elementary abelian $$p$$-group. A classification of finite groups $$G$$ with $$\omega(G)=3$$ will be given in this talk. As an "intermediate product", we also prove a conjecture posed by Gross in 1976.

Host: 谢贻林 Yilin Xie

Slides