Certain irreducible characters over a normal subgroup

TL;DR

This paper extends a key theorem on the solvability of groups of central type by incorporating automorphism actions and investigates induced characters with uniform constituent degrees.

Contribution

It introduces an extension of the Howlett-Isaacs theorem considering automorphisms and analyzes characters with all constituents sharing the same degree.

Findings

Extended the Howlett-Isaacs theorem to include automorphism actions.

Analyzed properties of induced characters with uniform constituent degrees.

Provided new insights into the structure of certain irreducible characters.

Abstract

We extend the Howlett-Isaacs theorem on the solvability of groups of central type taking into account actions by automorphisms. Then we study certain induced characters whose constituents have all the same degree.