Finite groups in which every irreducible character has either $p^{\prime }$-degree or $p^{\prime }$-codegree

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 $p^{\prime }$-degree or $p^{\prime }$-codegree.