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