Character degree sums of finite groups

TL;DR

This paper investigates the sums of character degrees in finite groups and explores their relationship with properties like solvability and nilpotency, providing new insights and strengthening existing results.

Contribution

It offers new results linking character degree sums to group properties and improves upon previous findings in the literature.

Findings

Character degree sums relate to p-solvability and solvability.

Strengthened known results on group properties.

Provides new bounds and relations involving character degrees.

Abstract

We present some results on character degree sums in connection with certain characteristics of finite groups such as p-solvability, solvability, supersolvability, and nilpotency. Some of them strengthen known results in the literature.