实现有限群的自动化

IF 0.4 3区 数学 Q4 MATHEMATICS Journal of Group Theory Pub Date : 2024-02-08 DOI:10.1515/jgth-2022-0145
Sylvia Bayard, Justin Lynd
{"title":"实现有限群的自动化","authors":"Sylvia Bayard, Justin Lynd","doi":"10.1515/jgth-2022-0145","DOIUrl":null,"url":null,"abstract":"It is shown that any finite group 𝐴 is realizable as the automizer in a finite perfect group 𝐺 of an abelian subgroup whose conjugates generate 𝐺. The construction uses techniques from fusion systems on arbitrary finite groups, most notably certain realization results for fusion systems of the type studied originally by Park.","PeriodicalId":50188,"journal":{"name":"Journal of Group Theory","volume":"69 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2024-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Realizing finite groups as automizers\",\"authors\":\"Sylvia Bayard, Justin Lynd\",\"doi\":\"10.1515/jgth-2022-0145\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"It is shown that any finite group 𝐴 is realizable as the automizer in a finite perfect group 𝐺 of an abelian subgroup whose conjugates generate 𝐺. The construction uses techniques from fusion systems on arbitrary finite groups, most notably certain realization results for fusion systems of the type studied originally by Park.\",\"PeriodicalId\":50188,\"journal\":{\"name\":\"Journal of Group Theory\",\"volume\":\"69 1\",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2024-02-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Group Theory\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/jgth-2022-0145\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Group Theory","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/jgth-2022-0145","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0

摘要

研究表明,任何有限群𝐴都可以实现为一个有限完全群𝐺的自动子群,其共轭子群生成𝐺。这个构造使用了任意有限群上融合系统的技术,其中最著名的是 Park 最初研究的那类融合系统的某些实现结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
Realizing finite groups as automizers
It is shown that any finite group 𝐴 is realizable as the automizer in a finite perfect group 𝐺 of an abelian subgroup whose conjugates generate 𝐺. The construction uses techniques from fusion systems on arbitrary finite groups, most notably certain realization results for fusion systems of the type studied originally by Park.
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
Journal of Group Theory
Journal of Group Theory 数学-数学
CiteScore
1.00
自引率
0.00%
发文量
45
审稿时长
6 months
期刊介绍: The Journal of Group Theory is devoted to the publication of original research articles in all aspects of group theory. Articles concerning applications of group theory and articles from research areas which have a significant impact on group theory will also be considered. Topics: Group Theory- Representation Theory of Groups- Computational Aspects of Group Theory- Combinatorics and Graph Theory- Algebra and Number Theory
期刊最新文献
On generalized concise words On 𝜎-permutable subgroups of 𝜎-soluble finite groups The commuting graph of a solvable 𝐴-group Root cycles in Coxeter groups Separability properties of nilpotent ℚ[𝑥]-powered groups II
×
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
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 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 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1