讲座题目1：群类理论中的若干公开问题

主讲人：李保军 教授

工作单位：南通大学

讲座时间：2020年9月22日 上午10:00-11:00

讲座形式：Zoom 会议室：********

内容简介：

A set X of groups is said to be a class if G∈X implies that H∈X for all groups H isomorphic to G. In this talk, we discuss on some questions related to the theory of classes of groups. These questions mainly include: the existence of covering subgroups and injectors;

modular law of fitting classes; the dual theory of a result of Bryce and Cossey and so on.

讲座人简介：

李保军，理学博士（中国科学技术大学），博士后（四川大学），南通大学教授。基础数学专业，主要从事群论方向研究，主持或参与国家自然科学基金多项，其中已主持完成面上项目和天元青年项目各1项。先后解决同行专家提出的关于“F-覆盖子群的存在性与共轭性”、“无核X-置换子群的超可解性”等多个公开问题，已在《中国科学A辑：数学》，《代数学杂志》（美）等国内外知名期刊发表论文40余篇。《美国数学评论》评论员，原四川省数学会理事。

讲座题目2：Normal p-complements and monomial characters

主讲人：陈晓友 博士

工作单位：河南工业大学

讲座时间：2020年9月29日 上午10:00-11:00

讲座形式：Zoom 会议室：********

内容简介:

Let G be a finite group, p be a prime and Irr(G) be the set of irreducible (complex) characters of G. We obtain a result about normal p-complements and monomial characters of G. This is joint work with prof. Yang.

讲座人简介：

陈晓友博士于2010年获得厦门大学博士学位，研究方向为群表示论，导师为曾吉文教授。现任教于河南工业大学理学院。于2016/01 - 2017/01访问美国肯特州立大学数学系，与国际知名群表示论专家Mark Lewis教授开展合作研究，取得了丰硕的研究成果。

讲座题目3：Prime divisors of element orders in finite solvable groups, I

讲座题目4：Prime divisors of element orders in finite solvable groups, II

主讲人：Thomas Keller 教授

工作单位：美国德克萨斯州立大学数学系

讲座时间：2020年10月13日 上午10:00-11:00

          2020年10月20日 上午10:00-11:00

讲座形式：Zoom 会议室：********

内容简介：

（1）Title: Prime divisors of element orders in finite solvable groups, I

Abstract: In these two talks we will study how the following problem: Given a finite group G, how is the number of distinct primes dividing |G| bounded in terms of the largest number of distinct primes dividing the order of an element of G? We will focus on solvable groups. For these,  Bannuscher/Tiedt and Zhang independently proved a quadratic upper bound and proved that if each element order is divisible by at most two different primes, then |G| is divisible by no more than than five different primes. In this first talk, we will focus on the small cases and discuss results for "three" and "four" instead of "two" above.

（2）Title: Prime divisors of element orders in finite solvable groups, II

Abstract: We continue the discussion of how many primes can occur in the order of a solvable group G if each element order is divisible by no more than n distinct primes. In this talk we focus on the asymptotic side of  things and present what is known on that.It turns out that the quadratic bound is not the best possible and that the true bound is linear. The conjecture is that 3n is an upper bound for the number of distinct primes occurring in |G|, but this is as of yet open.

讲座人简介：

Thomas Keller早年师从群论泰斗B. Huppert，1995年于德国Manz大学取得博士学位。现为德克萨斯州立大学终身正教授，在Adv. Math., J. Reine Angew. Math, J. Algebra等SCI顶级刊物上发表论文30余篇。Keller曾多次获得NSA以及Simons基金会的资助。