Title of the course: The number of conjugacy classes of finite groups
Instructor: Dr. Thomas Keller
Institution: Texas State University
Dates: 3-9 August 2026
Prerequisites: Students should be familiar with group theory, group actions, Sylow theorems etc.
Level: Graduate students or advanced undergraduate students
Abstract: In this course we will study conjugacy classes of finite groups with an emphasis on lower bounds for their number. Let k(G) denote the number of conjugacy classes of the finite group G. This is a fundamental parameter which has been studied from the beginnings of group theory. It is well-known that besides counting conjugacy classes, it also counts the number of irreducible complex representations of the group and thus can also be studied from this point of view. Over the years, many (upper and) lower bounds for k(G) have been proved, and the proofs touch on a lot of interesting mathematics. We will go into some of this in this course and also present some open problems.
Language: EN