Codegrees of primitive characters of solvable groups

TL;DR

This paper determines the codegree of specific primitive characters in finite solvable groups, providing a negative answer to a question posed by Moretó, thereby advancing understanding of character theory in group theory.

Contribution

It introduces the calculation of codegrees for certain primitive characters in solvable groups, addressing an open question in the field.

Findings

Identified the codegree of a specific primitive character in solvable groups.

Provided a negative answer to Moretó's question.

Enhanced understanding of character codegrees in group theory.

Abstract

We obtain the codegree of a certain primitive character for a finite solvable group, and thereby give a negative answer to a question proposed by Moret\'o in \cite{Moreto}.