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: Which maximal subgroups are perfect codes?
Speaker: 张志硕 Zhishuo Zhang (The University of Melbourne)
Time: 16:00-17:00 (GMT+8), Wednesday October 22nd
Location: Zoom: 262 780 8767 (passcode: gts2025)
Abstract:
A perfect code in a graph \(\Gamma=(V,E)\) is a subset \(C\) of \(V\) such that no two vertices in
\(C\) are adjacent and every vertex in \(V{\setminus}C\) is adjacent to exactly one vertex in \(C\).
A subgroup \(H\) of a group \(G\) is called a subgroup perfect code of \(G\) if it is a perfect code in some Cayley graph of \(G\).
In this talk, we initiate a study of which maximal subgroups of a group can occur as perfect codes.
We develop a general framework for this problem and propose several related questions.
The seminar is currently based at the Southern University of Science and Technology (SUSTech, 南方科技大学).