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: On fixer for finite Ree groups with solce \({}^2G_2(q)\)
Speaker: 谢贻林 Yilin Xie (SUSTech)
Time: 16:00-17:00 (GMT+8), Wednesday October 23rd
Location: Zoom: 856 490 7913 (passcode: gts2024)
Abstract:
Let \(G\) be a transitive permutation group on \(\Omega\). A subgroup \(K≤G\) is called a
fixer if each element in \(K\) fixes at least one point in \(\Omega\). A fixer \(K\) is called large
if \(K\geqslant |G_\omega|\). In this talk, I will sketch the proof of characterizing large fixers
for primitive actions of finite Ree groups with socle \({}^2G_2(q)\), where \(q=3^{2n+1}\), as part
of the project of characterizing large fixers for lie-type group of (twisted) rank 1.
In particular, I will first introduce the group \({}^2G_2(q)\), its subgroups, and conjugacy classes
of unipotent elements. Then we characterize the large fixers of primitive actions of \({}^2G_2(q)\)
by walking the subgroup lattice. We will study a family of additive subgroups of finite field \(F_q\)
and their intersection to eliminate one special case. Finally, we will involve in the field
automorphism and see which fixer of primitive actions of \({}^2G_2(q)\) can be extended to Aut\(({}^2G_2(q))\).
The seminar is currently based at the Southern University of Science and Technology (SUSTech, 南方科技大学).