群与图讨论班 Seminars on Groups and Graphs

这是群论和图论方向的线上系列报告，我们希望能够促进国内外青年学者（博士生为主）在群论和图论研究上的交流。报告主题分布在（但不限于）以下研究方向：

- 有限单群（有限单群分类定理，子群结构，共轭类等）
- 置换群及其在组合结构上的作用
- 线性代数群与李型群
- 有限群的表示
- 有限 $p$ -群
- 图的谱理论

This is a platform for young group theorists and graph theorists (mostly PhD students) to talk about their research and related topics online. The topic can be anything related to group theory and graph theory, including but not limited to the following.

- Finite simple groups (CFSG, subgroup structures and conjugacy classes)
- Permutation groups and their actions on combinatorial structures
- Linear algebraic groups and Lie type groups
- Representations of finite groups
- Finite $p$ -groups
- Spectral theory of graphs

Time

一般地，系列报告定期于北京时间每周三下午16:00-17:00进行。

Our usual time is Wednesday 16:00-17:00 (GMT+8).

Forthcoming Seminars

April 9th: Luca Sabatini (University of Warwick)
Arithmetical properties of subgroup products
Zoom: 262 780 8767 (passcode: gts2025)
April 29th: Marco Fusari (University of Milano-Bicocca)
TBD
Zoom: TBD
May 7th: 卢嘉平 Jiaping Lu (University of St. Andrews)
TBD
Zoom: TBD
May 14th: Pavel Turek (Royal Holloway, University of London)
TBD
Zoom: TBD
May 28th: 赵天骁 Tianxiao Zhao (Harbin)
TBD
Zoom: TBD

The Next Seminar

Title: Arithmetical properties of subgroup products

Speaker: Luca Sabatini (University of Warwick)

Time: 16:00-17:00 (GMT+8), Wednesday April 9th

Location: Zoom: 262 780 8767 (passcode: gts2025)

Abstract: Let $G$ be a finite group with a subgroup $H$ . If $H$ is subnormal, then $| H K |$ is a divisor of $| G |$ for any other subgroup $K$ . We observe that the Kegel-Wielandt-Kleidman theorem implies that the converse is also true, namely $| H K |$ divides $| G |$ for all $K$ if and only if $H$ is subnormal. Some interesting phenomena are related. For example, $x^{| G : K |} \in K$ for all subgroups $K$ if and only if $x$ lies in the Fitting subgroup.

Other Confirmed Speakers

Jan Petr (University of Cambridge)
颜全福 Quanfu Yan (Peking University)

Current Organizers

陈俊彦 Junyan Chen (SUSTech)
尹富纲 Fu-Gang Yin (Beijing Jiaotong University)
张宝羽 Baoyu Zhang (University of Birmingham)

The seminar is currently based at the Southern University of Science and Technology (SUSTech, 南方科技大学).