{"title":"所有渐开线都是 3 变换的群","authors":"Egle Bettio, Enrico Jabara","doi":"10.1007/s00605-023-01941-z","DOIUrl":null,"url":null,"abstract":"<p>Let <i>G</i> be a group which is generated by the set of its involutions, and assume that the set of integers which occur as orders of products of two involutions in <i>G</i> is <span>\\(\\{1,2,3,4\\}\\)</span>. It is shown that <span>\\(G\\simeq \\textrm{PSL}(2,7)\\)</span> or <span>\\(G\\simeq \\textrm{PSU}(3,3)\\)</span> or <i>G</i> is a <span>\\(\\{2,3\\}\\)</span>-group and <span>\\(G/O_{2}(G) \\simeq S_{3}\\)</span>.\n</p>","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Groups in which all involutions are 3-transvections\",\"authors\":\"Egle Bettio, Enrico Jabara\",\"doi\":\"10.1007/s00605-023-01941-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Let <i>G</i> be a group which is generated by the set of its involutions, and assume that the set of integers which occur as orders of products of two involutions in <i>G</i> is <span>\\\\(\\\\{1,2,3,4\\\\}\\\\)</span>. It is shown that <span>\\\\(G\\\\simeq \\\\textrm{PSL}(2,7)\\\\)</span> or <span>\\\\(G\\\\simeq \\\\textrm{PSU}(3,3)\\\\)</span> or <i>G</i> is a <span>\\\\(\\\\{2,3\\\\}\\\\)</span>-group and <span>\\\\(G/O_{2}(G) \\\\simeq S_{3}\\\\)</span>.\\n</p>\",\"PeriodicalId\":18913,\"journal\":{\"name\":\"Monatshefte für Mathematik\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-01-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Monatshefte für Mathematik\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s00605-023-01941-z\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Monatshefte für Mathematik","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s00605-023-01941-z","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
让 G 是一个由它的渐开线集合生成的群，并假设在 G 中作为两个渐开线乘积的阶出现的整数集合是 （ （ （{1,2,3,4\}\））。证明了\(G\simeq \textrm{PSL}(2,7)\) 或\(G\simeq \textrm{PSU}(3,3)\) 或 G 是一个\(\{2,3\})-群，并且\(G/O_{2}(G) \simeq S{3}/)。
Groups in which all involutions are 3-transvections
Let G be a group which is generated by the set of its involutions, and assume that the set of integers which occur as orders of products of two involutions in G is \(\{1,2,3,4\}\). It is shown that \(G\simeq \textrm{PSL}(2,7)\) or \(G\simeq \textrm{PSU}(3,3)\) or G is a \(\{2,3\}\)-group and \(G/O_{2}(G) \simeq S_{3}\).
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