On permutation characters of finite group

Jiakuan Lu; hangyang Meng

On permutation characters of finite group

Group Theory 2026-03-31 v2

Authors: Jiakuan Lu , hangyang Meng

Abstract

Let $G$ be a finite group and $M$ be a maximal subgroup of $G$ . We call every irreducible constituent $\chi$ of $(1_M)^G$ a $\mathcal{P}$ -character of $G$ with respect to $M$ . In this paper, we prove that all $\mathcal{P}$ -characters of $G$ are monomial if and only if $G$ is solvable, which solves a question posed by Qian and Yang.

Keywords

finite group permutation character irreducible constituent monomial representation solvable group

Cite

@article{arxiv.2511.20171,
  title  = {On permutation characters of finite group},
  author = {Jiakuan Lu and hangyang Meng},
  journal= {arXiv preprint arXiv:2511.20171},
  year   = {2026}
}

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