Galois Conjugacy and Fitting Height 2: Classification of Finite Solvable Groups

Abstract

This paper investigates the finite groups 𝐺 for which any two characters in the set of irreducible complex characters 𝑰𝒓𝒓(𝐺) are Galois conjugate. Specifically, we classify such groups and establish a key result: they are solvable with Fitting height 2. The analysis involves intricate considerations of irreducible complex characters and their Galois conjugacy, shedding light on the structural properties of finite solvable groups.