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April 10th

# Finite linear groups with exactly three orbits

## 伊涵玥 Hanyue Yi

SUSTech

Time: 16:00-17:00 (GMT+8), Wednesday April 10th, 2024

Location: Zoom

**Abstract:**
Let \(V\) be a finite vector space over a field of prime order.
Recall that a remarkable result of Hering in 1985 classifies the subgroups of \(\mathrm{GL}(V)\) which act transitively on non-zero vectors.
Later in 1987, Liebeck gave a complete classification of irreducible subgroups of \(\mathrm{GL}(V)\) with exactly \(3\) orbits on \(V\).
In this talk, we analyze reducible subgroups of \(\mathrm{GL}(V)\) with exactly \(3\) orbits, which is a step towards a classification of finite permutation groups of rank \(3\).
Joint work with Cai Heng Li and Yan Zhou Zhu.

Host: 黄弘毅 Hong Yi Huang

Slides