The character degree ratio and composition factors of a finite group

TL;DR

This paper establishes an upper bound on the number of non-abelian composition factors of a finite group based on the ratio of degrees of its nonlinear irreducible characters, linking character theory to group structure.

Contribution

It provides a new quantitative bound connecting the character degree ratio to the composition factors of finite groups, advancing understanding of their structure.

Findings

Number of non-abelian composition factors ≤ 1.8 * ln(rat(G)) + 1.3

Introduces a bound relating character degree ratios to group composition

Enhances the link between character theory and group structure

Abstract

For a finite non-abelian group $G$ let $\rat(G)$ denote the largest ratio of degrees of two nonlinear irreducible characters of $G$. We prove that the number of non-abelian composition factors of $G$ is bounded above by $1.8\ln(\rat(G))+1.3$.