Methods and questions in character degrees of finite groups

TL;DR

This paper reviews key open problems in the character degrees of finite groups, discussing various methods and their applications to related problems involving character zeros, kernels, and fields of values.

Contribution

It compiles and discusses useful methods for tackling open problems in character degrees and related character theory issues in finite groups.

Findings

Collected effective methods for studying character degrees.

Applied methods to problems on zeros, kernels, and fields of characters.

Provided insights into open problems in finite group character theory.

Abstract

We present some variations on some of the main open problems on character degrees. We collect some of the methods that have proven to be very useful to work on these problems. These methods are also useful to solve certain problems on zeros of characters, character kernels and fields of values of characters.