特殊的大厅数字

Zheng Guo, Yong Hu, Cai Heng Li
{"title":"特殊的大厅数字","authors":"Zheng Guo, Yong Hu, Cai Heng Li","doi":"arxiv-2408.03184","DOIUrl":null,"url":null,"abstract":"A positive integer $m$ is called a Hall number if any finite group of order\nprecisely divisible by $m$ has a Hall subgroup of order $m$. We prove that,\nexcept for the obvious examples, the three integers $12$, $24$ and $60$ are the\nonly Hall numbers, solving a problem proposed by Jiping Zhang.","PeriodicalId":501037,"journal":{"name":"arXiv - MATH - Group Theory","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The exceptional Hall numbers\",\"authors\":\"Zheng Guo, Yong Hu, Cai Heng Li\",\"doi\":\"arxiv-2408.03184\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A positive integer $m$ is called a Hall number if any finite group of order\\nprecisely divisible by $m$ has a Hall subgroup of order $m$. We prove that,\\nexcept for the obvious examples, the three integers $12$, $24$ and $60$ are the\\nonly Hall numbers, solving a problem proposed by Jiping Zhang.\",\"PeriodicalId\":501037,\"journal\":{\"name\":\"arXiv - MATH - Group Theory\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Group Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2408.03184\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Group Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.03184","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

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。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信