# 群与图讨论班 Seminars on Groups and Graphs

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# The $$\mathcal{C}_6$$ subgroups of finite classical groups

## 谢贻林 Yilin Xie

SUSTech

Time: 16:00-18:00 (GMT+8), Tuesday March 8th, 2022
Location: Tencent Meeting

Abstract: A $$\mathcal{C}_6$$ subgroup of a simple classical group is the normalizer of a symplectic-type $$r$$-group of minimal exponent (modulo scalars). We will first learn the structure of the symplectic-type $$r$$-groups and their automorphism groups. Then we learn the representation of these groups over $$\mathbb{C}$$ and finite fields. Finally, we embed a symplectic-type $$r$$-group in a linear group $$G$$ and find the structure of its normalizer (modulo scalar) in $$G$$.

Host: 黄弘毅 Hong Yi Huang

Slides