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Southern University of Science and Technology

Time: 16:00-17:00 (GMT+8), Wednesday October 23rd, 2024

Location: Zoom

**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\(({}^2G_2(q))\).

Host: 陈俊彦 Junyan Chen