The exceptional Hall numbers
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2024
- DOI:
- 10.48550/arXiv.2408.03184
- arXiv:
- arXiv:2408.03184
- Bibcode:
- 2024arXiv240803184G
- Keywords:
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- Mathematics - Group Theory
- E-Print:
- 7 pages