Representations and characters have been proved to be very useful tools to study finite groups. I will discuss some results on the relationship between fields of values of characters of a finite group and the structure of the group, from a classical result of Burnside on real-valued characters and Navarro-Tiep’s result on rational-valued characters of odd degree to very recent results of my collaborators and myself on (almost) p-rational characters.
This video is part of the University of Georgia‘s Algebra seminar.
