A Krull–Remak–Schmidt theorem for fusion systems

IF 0.5 3区 数学 Q3 MATHEMATICS
B. Oliver
{"title":"A Krull–Remak–Schmidt theorem for fusion systems","authors":"B. Oliver","doi":"10.4064/fm160-5-2022","DOIUrl":null,"url":null,"abstract":"We prove that the factorization of a saturated fusion system over a discrete $p$-toral group as a product of indecomposable subsystems is unique up to normal automorphisms of the fusion system and permutations of the factors. In particular, if the fusion system has trivial center, or if its focal subgroup is the entire Sylow group, then this factorization is unique (up to the ordering of the factors). This result was motivated by questions about automorphism groups of products of fusion systems.","PeriodicalId":55138,"journal":{"name":"Fundamenta Mathematicae","volume":" ","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2021-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fundamenta Mathematicae","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4064/fm160-5-2022","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 2

Abstract

We prove that the factorization of a saturated fusion system over a discrete $p$-toral group as a product of indecomposable subsystems is unique up to normal automorphisms of the fusion system and permutations of the factors. In particular, if the fusion system has trivial center, or if its focal subgroup is the entire Sylow group, then this factorization is unique (up to the ordering of the factors). This result was motivated by questions about automorphism groups of products of fusion systems.
聚变系统的Krull–Remak–Schmidt定理
我们证明了作为不可分解子系统的乘积的离散$p$-toral群上的饱和融合系统的因子分解对于融合系统的正规自同构和因子的排列是唯一的。特别地,如果融合系统具有平凡中心,或者如果它的焦点子群是整个Sylow群,那么这个因子分解是唯一的(直到因子的排序)。这一结果的动机是关于融合系统乘积的自同构群的问题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
Fundamenta Mathematicae
Fundamenta Mathematicae 数学-数学
CiteScore
1.00
自引率
0.00%
发文量
44
审稿时长
6-12 weeks
期刊介绍: FUNDAMENTA MATHEMATICAE concentrates on papers devoted to Set Theory, Mathematical Logic and Foundations of Mathematics, Topology and its Interactions with Algebra, Dynamical Systems.
×
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