特殊的大厅数字

arXiv - MATH - Group Theory Pub Date : 2024-08-06 DOI:arxiv-2408.03184

Zheng Guo, Yong Hu, Cai Heng Li

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摘要

如果任何阶精确可被 $m$ 整除的有限群都有一个阶为 $m$ 的霍尔子群，那么正整数 $m$ 就被称为霍尔数。我们证明，除了明显的例子之外，$12$, $24$ 和 $60$ 这三个整数是唯一的霍尔数，解决了张继平提出的一个问题。

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The exceptional Hall numbers

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.

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arXiv - MATH - Group Theory

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