讲座题目：Conjugacy classes of p-elements and normal p-complements

主办单位：三峡数学研究中心/理学院

报告专家：Hung P. Tong-Viet

报告时间：2023年3月28日（周二）上午（8:30-11:30）

报告地点：Zoom会议（ID：871 1750 2061 密码：666888)

专家简介：Hung P. Tong-Viet，Ph.D., 2009, University of Birmingham (UK)，现为美国 Binghamton University 副教授。群论杂志编辑，在高级别杂志发表文章60多篇。早期工作解决了Huppert刻画单群的猜想的弱形式（包含特征标重数），也对部分低阶李型单群证明了Huppert刻画单群的猜想。在2017年与张继平院士合作证明了Huppert刻画单群猜想的所有交错群情况。近期对于实共轭类与实特征标的算术性质也颇有建树。

报告摘要：The commuting probability d(G) of a finite group G (introduced by Erdös and Turán in 1968), is defined to be the probability that two randomly chosen elements of G commute. The commuting probability d(G) is also called the commutativity degree of G. Erdös and Turán show that d(G)=k(G)/|G|, where k(G) is number of conjugacy classes of G. In 1973, W. H. Gustafson proved that d(G)≤5/8 for any non-abelian group G. Since then, there are numerous results concerning the structure of finite groups using various bounds on the commuting probability. In this talk, I will consider a p-local version of the commuting probability. Specifically, for a prime p, we define d_p(G) to be the ratio k_p(G)/|G|, where k_p(G) is the number of conjugacy classes of p-elements of G and P is a Sylow p-subgroup of G. Using the invariant d_p(G), we obtain some new criteria for the existence of normal p-complements in finite groups.