Simple groups, Sylow subgroups and intersections

报告人：黄弘毅（匈牙利阿尔弗雷德·雷尼数学研究所）

时  间：2026年9月23日10:00

地  点：海韵园实验楼S307

内容摘要:

Given a finite group G and a prime p, when can we find two Sylow p-subgroups that intersect trivially? If G is simple, then a theorem of Mazurov and Zenkov from 1996 shows that this question has a positive answer for every prime p, and their proof uses earlier work on defect groups of p-blocks for simple groups of Lie type.

In this talk, we will apply a probabilistic approach to study the intersections of randomly chosen Sylow subgroups. For non-alternating simple groups, we will use this tool to verify a very recent conjecture of Lisi and Sabatini on "synchronised intersections" of Sylow subgroups. In addition, our approach allows us to give an independent proof of Mazurov-Zenkov theorem for these groups, and we are able to complete the proof of a strong form of a conjecture of Vdovin from 2002 on intersections of nilpotent subgroups of simple groups. Along the way, we establish new asymptotic results on the probability that two random Sylow p-subgroups in a simple group of Lie type have trivial intersection, complementing recent work of Diaconis et al. and Eberhard on symmetric and alternating groups.

Joint work with Tim Burness (Bristol).

个人简介：

黄弘毅，匈牙利阿尔弗雷德·雷尼数学研究所（Alfréd Rényi Institute of Mathematics）研究员。2025 年博士毕业于英国布里斯托大学。研究领域为群论与代数组合，主要关注有限置换群与有限单群。在置换群的基（base）、Saxl 图，几乎单群中 Sylow 子群与幂零子群之交和三阶秩置换群的分类等诸多问题上都取得了原创性成果，论文发表在 Proc. Lond. Math. Soc., Forum Math. Sigma, J. Algebra, Algebr. Comb., J. Pure Appl. Algebra 等重要期刊上。

联系人：朱砚舟