A generalization of the Arad--Ward theorem on Hall subgroups
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909453631094784 |
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| author | Yang, N. Buturlakin, A. A. |
| author_facet | Yang, N. Buturlakin, A. A. |
| contents | For a set of primes $π$, denote by $E_π$ the class of finite groups containing a Hall $π$-subgroup. We establish that $E_{π_1}\cap E_{π_2}$ is contained in $E_{π_1\capπ_2}$. As a corollary, we prove that if $π$ is a set of primes, $l$ is an integer such that $2\leqslant l<|π|$ and $G$ is a finite group that contains a Hall $ρ$-subgroup for every subset $ρ$ of $π$ of size $l$, then $G$ contains a solvable Hall $π$-subgroup. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_05865 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A generalization of the Arad--Ward theorem on Hall subgroups Yang, N. Buturlakin, A. A. Group Theory 20D20, 20D30 For a set of primes $π$, denote by $E_π$ the class of finite groups containing a Hall $π$-subgroup. We establish that $E_{π_1}\cap E_{π_2}$ is contained in $E_{π_1\capπ_2}$. As a corollary, we prove that if $π$ is a set of primes, $l$ is an integer such that $2\leqslant l<|π|$ and $G$ is a finite group that contains a Hall $ρ$-subgroup for every subset $ρ$ of $π$ of size $l$, then $G$ contains a solvable Hall $π$-subgroup. |
| title | A generalization of the Arad--Ward theorem on Hall subgroups |
| topic | Group Theory 20D20, 20D30 |
| url | https://arxiv.org/abs/2501.05865 |