A characterization of finite groups by certain Galois conjugacy class of irreducible characters

TL;DR

This paper classifies finite groups based on a specific Galois conjugacy property of their irreducible characters, revealing structural insights into their character theory.

Contribution

It provides a complete classification of finite groups where certain irreducible characters form a single Galois conjugacy class under specified conditions.

Findings

Finite groups satisfying the Galois conjugacy condition are fully characterized.

The classification links character degrees and kernel indices.

The work advances understanding of the interplay between group structure and character field automorphisms.

Abstract

We classify the finite groups $G$ which satisfies the condition that every complex irreducible character,whose degree's square doesn't divide the index of its kernel in $G$, lies in the same Galois conjugacy class.