{"title":"有限群的非平凡真子群的有限空间","authors":"Lingling Han, Tao Zheng","doi":"10.1016/j.jpaa.2025.107894","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we investigate the homotopy properties of <span><math><mi>L</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span>, the finite topological space consisting of all non-trivial proper subgroups of a finite group <em>G</em>. For some classes of groups <em>G</em>, we give the relations between the contractibility of <span><math><mi>L</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> and the algebraic properties of <em>G</em>, which is inspired by the study of R. E. Stong on <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo></math></span> and <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo></math></span>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 2","pages":"Article 107894"},"PeriodicalIF":0.8000,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the finite spaces of non-trivial proper subgroups of finite groups\",\"authors\":\"Lingling Han, Tao Zheng\",\"doi\":\"10.1016/j.jpaa.2025.107894\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In this paper, we investigate the homotopy properties of <span><math><mi>L</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span>, the finite topological space consisting of all non-trivial proper subgroups of a finite group <em>G</em>. For some classes of groups <em>G</em>, we give the relations between the contractibility of <span><math><mi>L</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> and the algebraic properties of <em>G</em>, which is inspired by the study of R. E. Stong on <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo></math></span> and <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo></math></span>.</div></div>\",\"PeriodicalId\":54770,\"journal\":{\"name\":\"Journal of Pure and Applied Algebra\",\"volume\":\"229 2\",\"pages\":\"Article 107894\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2025-02-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Pure and Applied Algebra\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0022404925000337\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2025/1/23 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Pure and Applied Algebra","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022404925000337","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/1/23 0:00:00","PubModel":"Epub","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
本文研究了由有限群G的所有非平凡真子群组成的有限拓扑空间L(G)的同伦性质。对于群G的某些类，我们得到了R. E. strong关于Sp(G)和Ap(G)的研究的启发，给出了L(G)的可缩并性与G的代数性质之间的关系。
On the finite spaces of non-trivial proper subgroups of finite groups
In this paper, we investigate the homotopy properties of , the finite topological space consisting of all non-trivial proper subgroups of a finite group G. For some classes of groups G, we give the relations between the contractibility of and the algebraic properties of G, which is inspired by the study of R. E. Stong on and .
期刊介绍：
The Journal of Pure and Applied Algebra concentrates on that part of algebra likely to be of general mathematical interest: algebraic results with immediate applications, and the development of algebraic theories of sufficiently general relevance to allow for future applications.
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