On Distinct Character Degrees

TL;DR

This paper extends a characterization of finite groups with distinct nonlinear irreducible character degrees to a broader class of solvable groups with a specific normal subgroup, revealing new structural insights.

Contribution

It generalizes previous results by characterizing solvable groups with a normal subgroup where certain irreducible characters have distinct degrees.

Findings

Characterization of solvable groups with a normal subgroup and distinct degrees

Extension of previous group character degree results

Broader understanding of irreducible character degree distributions

Abstract

Berkovich, Chillag and Herzog characterized all finite groups $G$ in which all the nonlinear irreducible characters of $G$ have distinct degrees. In this paper we extend this result showing that a similar characterization holds for all finite solvable groups $G$ that contain a normal subgroup $N$, such that all the irreducible characters of $G$ that do not contain $N$ in their kernel have distinct degrees.