Monomial characters of finite solvable groups

TL;DR

This paper investigates how the structure of finite solvable groups can be understood through irreducible monomial characters, providing new insights into longstanding conjectures in group theory.

Contribution

It offers new evidence on the role of monomial characters in understanding solvable groups and their relation to key conjectures like Isaacs-Navarro-Wolf and Gluck's conjecture.

Findings

Monomial characters influence the structure of solvable groups

New evidence supporting the role of monomial characters in key conjectures

Insights into the relationship between characters and group structure

Abstract

We give new evidences to the fact that the structure of a solvable group can be controlled by irreducible monomial characters. In particular we inspect the role of monomial characters in Isaacs-Navarro-Wolf's conjecture and in Gluck's conjecture.