Finite groups whose non-linear irreducible characters of the same degree are Galois conjugate

TL;DR

This paper classifies finite groups based on the Galois conjugacy of their non-linear irreducible characters with distinct degrees, extending previous classification results.

Contribution

It provides a complete classification of finite groups with non-linear irreducible characters that are Galois conjugate and have distinct degrees, expanding earlier work.

Findings

Classification of such finite groups

Extension of previous classification results

Character degree and Galois conjugacy relationship

Abstract

We classify the finite groups whose non-linear irreducible characters that are not conjugate under the natural Galois action have distinct degrees, therefore extending the results in Berkovich et al. [Proc. Amer. Math. Soc. {\bf 115} (1992), 955-959] and Dolfi et al. [Israel J. Math. {\bf 198} (2013), 283-331].