{"title":"关于经典简单群的高尔斯诀窍","authors":"Francesco Fumagalli , Attila Maróti","doi":"10.1016/j.jpaa.2024.107833","DOIUrl":null,"url":null,"abstract":"<div><div>If <em>A</em>, <em>B</em>, <em>C</em> are subsets in a finite simple group of Lie type <em>G</em> at least two of which are normal with <span><math><mo>|</mo><mi>A</mi><mo>|</mo><mo>|</mo><mi>B</mi><mo>|</mo><mo>|</mo><mi>C</mi><mo>|</mo></math></span> relatively large, then we establish a stronger conclusion than <span><math><mi>A</mi><mi>B</mi><mi>C</mi><mo>=</mo><mi>G</mi></math></span>. This is related to a theorem of Gowers and is a generalization of a theorem of Larsen, Shalev, Tiep and the second author and Pyber.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 1","pages":"Article 107833"},"PeriodicalIF":0.7000,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the Gowers trick for classical simple groups\",\"authors\":\"Francesco Fumagalli , Attila Maróti\",\"doi\":\"10.1016/j.jpaa.2024.107833\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>If <em>A</em>, <em>B</em>, <em>C</em> are subsets in a finite simple group of Lie type <em>G</em> at least two of which are normal with <span><math><mo>|</mo><mi>A</mi><mo>|</mo><mo>|</mo><mi>B</mi><mo>|</mo><mo>|</mo><mi>C</mi><mo>|</mo></math></span> relatively large, then we establish a stronger conclusion than <span><math><mi>A</mi><mi>B</mi><mi>C</mi><mo>=</mo><mi>G</mi></math></span>. This is related to a theorem of Gowers and is a generalization of a theorem of Larsen, Shalev, Tiep and the second author and Pyber.</div></div>\",\"PeriodicalId\":54770,\"journal\":{\"name\":\"Journal of Pure and Applied Algebra\",\"volume\":\"229 1\",\"pages\":\"Article 107833\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-10-28\",\"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/S0022404924002305\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"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/S0022404924002305","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
如果 A、B、C 是有限简单李型群 G 中的子集，其中至少有两个子集是正常的，且 |A||B||C|| 相对较大，那么我们就建立了比 ABC=G 更强的结论。
If A, B, C are subsets in a finite simple group of Lie type G at least two of which are normal with relatively large, then we establish a stronger conclusion than . This is related to a theorem of Gowers and is a generalization of a theorem of Larsen, Shalev, Tiep and the second author and Pyber.
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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