A new generalization of the McKay conjecture for $p$-solvable groups
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915661765148672 |
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| author | Chang, Huimin Jin, Ping |
| author_facet | Chang, Huimin Jin, Ping |
| contents | Let $P$ be a Sylow $p$-subgroup of a finite $p$-solvable group $G$, where $p$ is a prime. Using a normal $p$-series $\mathcal{N}$ of $G$, we introduce the notion of $(\mathcal{N},p)$-stable characters and prove that $G$ and ${\bf N}_G(P)$ have equal numbers of such characters, which gives a new generalization of the McKay conjecture for $p$-solvable groups. Also, we establish a canonical bijection between these characters in the case where $G$ has odd order. Our proofs depend heavily on the theory of self-stabilizing pairs founded by M. L. Lewis, as well as some results of $π$-special characters due to I. M. Isaacs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_07073 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A new generalization of the McKay conjecture for $p$-solvable groups Chang, Huimin Jin, Ping Group Theory 20C15 Let $P$ be a Sylow $p$-subgroup of a finite $p$-solvable group $G$, where $p$ is a prime. Using a normal $p$-series $\mathcal{N}$ of $G$, we introduce the notion of $(\mathcal{N},p)$-stable characters and prove that $G$ and ${\bf N}_G(P)$ have equal numbers of such characters, which gives a new generalization of the McKay conjecture for $p$-solvable groups. Also, we establish a canonical bijection between these characters in the case where $G$ has odd order. Our proofs depend heavily on the theory of self-stabilizing pairs founded by M. L. Lewis, as well as some results of $π$-special characters due to I. M. Isaacs. |
| title | A new generalization of the McKay conjecture for $p$-solvable groups |
| topic | Group Theory 20C15 |
| url | https://arxiv.org/abs/2512.07073 |