{"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":"22 1","pages":""},"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}
引用次数: 0
Abstract
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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