# Solvable groups whose monomial, monolithic characters have prime power codegrees

Document Type : Research Paper

Authors

1 School of Sciences, Henan University of Technology, P.O.Box 450001, Zhengzhou, China

2 Department of Mathematical Sciences, Kent State University, P.O.Box 44242, Kent, USA

Abstract

In this note, we prove that if $G$ is solvable and ${\rm cod}(\chi)$ is a $p$-power for every nonlinear, monomial, monolithic $\chi\in {\rm Irr}(G)$ or every nonlinear, monomial, monolithic $\chi \in {\rm IBr} (G)$, then $P$ is normal in $G$, where $p$ is a prime and $P$ is a Sylow $p$-subgroup of $G$.

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