Title: On Groups with the Same Index Set as Nilpotent Groups

Speaker: Wei Zhou, Doctoral Student (Sobolev Institute of Mathematics, Russia)

Time: July 29, 2025, 16:30-17:30

Venue: Room B303, School of Mathematics

Abstract:

This talk focuses on the relationship between the index set (i.e., the set of conjugacy class sizes) and the structure of finite groups, addressing two open questions posed by Camina in 2006:

1. Constructing a series of finite groups that share the same index set as nilpotent groups but have trivial centers, providing counterexamples to one of Camina’s questions.

2. Establishing a necessary and sufficient condition for an A-group to be abelian based on its index set, completely resolving another question.

About the Speaker:

Wei Zhou is a doctoral student at the Sobolev Institute of Mathematics, Russia. His research interests lie in finite group theory, with a focus on the relationship between conjugacy class sizes and group structure in finite groups.

All interested faculty and students are welcome to attend and participate in discussions.