Speaker：Hongyi Huang (HUN-REN Alfréd Rényi Institute of Mathematics)

Time：2026-9-23 10:00

Location：Conference Room S307 at Experiment Building at Haiyun Campus

Abstract:

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).