Finite groups in which every irreducible character has either $p'$-degree or $p'$-codegree

TL;DR

This paper classifies finite groups where each irreducible character has either degree or codegree coprime to a prime p, revealing structural properties related to character theory.

Contribution

It provides a complete classification of such groups, connecting character degrees and codegrees with group structure for a fixed prime p.

Findings

Character degrees are either p'-numbers or p'-codegrees in classified groups

Structural properties of groups are determined by the character degree and codegree conditions

The classification aids in understanding the interplay between group structure and character theory

Abstract

For an irreducible complex character $\chi$ of a finite group $G$, the codegree of $\chi$ is defined by $|G:\ker(\chi)|/\chi(1)$, where $\ker(\chi)$ is the kernel of $\chi$. Given a prime $p$, we provide a classification of finite groups in which every irreducible complex character has either $p'$-degree or $p'$-codegree.