讲座题目：On Groups with the Same Index Set as Nilpotent Groups

主 讲 人：周伟 博士研究生（俄罗斯科学院索伯列夫数学研究所）

讲座时间：2025年7月1日（周二）10：00-11：00

讲座地点：理学院109会议室

欢迎有兴趣的师生前来聆听、交流。

理学院

2025年6月24日

讲座内容简介：

In this talk, we will present two results concerning the relationship between the index set and the structure of finite groups, which together answer two open questions posed by Camina in 2006. Here, the index set refers to the set of conjugacy class sizes of a group. We construct a series of finite groups that share the same index set as nilpotent groups but have trivial center, thereby providing counterexamples to one of Camina’s questions. Moreover, we obtain a necessary and sufficient condition for an A-group to be abelian, based on its index set. This result completely resolves another question posed by Camina.

主讲人简介：

周伟，俄罗斯科学院索伯列夫数学研究所博士研究生，主要研究方向为有限群论，目前的研究重点是有限群的共轭类大小与群结构之间的关系。