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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.03184 |
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| _version_ | 1866910557796302848 |
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| author | Guo, Zheng Hu, Yong Li, Cai Heng |
| author_facet | Guo, Zheng Hu, Yong Li, Cai Heng |
| contents | A positive integer $m$ is called a Hall number if any finite group of order precisely divisible by $m$ has a Hall subgroup of order $m$. We prove that, except for the obvious examples, the three integers $12$, $24$ and $60$ are the only Hall numbers, solving a problem proposed by Jiping Zhang. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_03184 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The exceptional Hall numbers Guo, Zheng Hu, Yong Li, Cai Heng Group Theory A positive integer $m$ is called a Hall number if any finite group of order precisely divisible by $m$ has a Hall subgroup of order $m$. We prove that, except for the obvious examples, the three integers $12$, $24$ and $60$ are the only Hall numbers, solving a problem proposed by Jiping Zhang. |
| title | The exceptional Hall numbers |
| topic | Group Theory |
| url | https://arxiv.org/abs/2408.03184 |