The interaction between character degrees and the structure of finite groups has been a topic of interest for a long time, dating back to the influential work of I. M. Isaacs and D. S. Passman in the sixties. In this line of research, one often considers an invariant concerning character degrees and studies how it reflects or is reflected by the group. One of those invariants is the average character degree.

We will present some new results concerning the average character degrees which generalize some earlier classical results of Thompson and Ito-Michler and more recent results of Isaacs-Loukaki-Moreto and Navarro-Tiep.
Speaker(s): Hung Ngoc Nguyen (University of Akron)