Solvable groups whose monomial, monolithic characters have prime power codegrees

Xiaoyou Chen; Mark L. Lewis

Solvable groups whose monomial, monolithic characters have prime power codegrees

Representation Theory 2022-11-16 v1

Authors: Xiaoyou Chen , Mark L. Lewis

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 $G$ .

Keywords

finite groups

Cite

@article{arxiv.2211.08178,
  title  = {Solvable groups whose monomial, monolithic characters have prime power codegrees},
  author = {Xiaoyou Chen and Mark L. Lewis},
  journal= {arXiv preprint arXiv:2211.08178},
  year   = {2022}
}

Comments

To appear in International Journal of Group Theory

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