必赢体育

报告题目：Intersections of Sylow subgroups in simple groups

主讲人：黄弘毅博士（南方科技大学）

时间：2025年12月23日（周二）10:00 a.m.

地点：北院卓远楼305会议室

主办单位：统计与数学学院

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 p-subgroups. For non-alternating simple groups, we will use this tool to verify an interesting conjecture of Lisi and Sabatini (2025) on “synchronised intersections” of Sylow subgroups. In addition, Our method yields a new proof of the Mazurov-Zenkov theorem for these groups. Moreover, by combining our results with earlier work of Kurmazov from 2013, we complete the proof of a strong form of a conjecture of Vdovin from 2002 on intersections of nilpotent subgroups of simple groups, which is stated as Problem 15.40 in the Kourovka Notebook. 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. (2025) and Eberhard (2025) on symmetric and alternating groups.

 Joint work with Tim Burness (University of Bristol, UK).

主讲人简介：

黄弘毅，男，27岁，2025年于University of Bristol取得博士学位，现为南方科技大学高级研究学者。研究方向为群论，特别是单群、置换群以及在代数组合的应用。2025年3月受邀参加于德国Oberwolfach（黑森林数学中心）举行的短期研讨会并做邀请报告，同年获“伦敦数学会青年学者”。在Forum of Mathematics, Sigma，Journal of Algebra等期刊发表多篇论文。