On permutation characters of finite group

Jiakuan Lu; hangyang Meng

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arXiv · 2511.20171

On permutation characters of finite group

Jiakuan Lu·hangyang Meng

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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.

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BibTeX RIS

Jiakuan Lu, hangyang Meng. 2025-11-25. On permutation characters of finite group. https://arxiv.org/abs/2511.20171

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