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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2410.07556 |
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| _version_ | 1866929537491664896 |
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| author | Wu, Zongshu Yang, Yong |
| author_facet | Wu, Zongshu Yang, Yong |
| contents | Let $G$ be a finite group, and $π$ be a set of primes. The $π$-core $\mathbf{O}_π(G)$ is the unique maximal normal $π$-subgroup of $G$, and $b(G)$ is the largest irreducible character degree of $G$. In 2017, Qian and Yang proved that if $H$ is a solvable $π$-subgroup of $G$, then $|H\mathbf{O}_π(G)/\mathbf{O}_π(G)|\le b(G)^3$. In this paper, we improve the exponent of $3$ to $3\log_{504}(168)<2.471$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_07556 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On The Largest Character Degree And Solvable Subgroups Of Finite Groups Wu, Zongshu Yang, Yong Group Theory Let $G$ be a finite group, and $π$ be a set of primes. The $π$-core $\mathbf{O}_π(G)$ is the unique maximal normal $π$-subgroup of $G$, and $b(G)$ is the largest irreducible character degree of $G$. In 2017, Qian and Yang proved that if $H$ is a solvable $π$-subgroup of $G$, then $|H\mathbf{O}_π(G)/\mathbf{O}_π(G)|\le b(G)^3$. In this paper, we improve the exponent of $3$ to $3\log_{504}(168)<2.471$. |
| title | On The Largest Character Degree And Solvable Subgroups Of Finite Groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2410.07556 |