{"title":"Hall’s universal group is a subgroup of the abstract commensurator of a free group","authors":"Edgar A. Bering, Daniel Studenmund","doi":"10.1007/s11856-023-2591-8","DOIUrl":null,"url":null,"abstract":"<p>P. Hall constructed a universal countable locally finite group <i>U</i>, determined up to isomorphism by two properties: every finite group <i>C</i> is a subgroup of <i>U</i>, and every embedding of <i>C</i> into <i>U</i> is conjugate in <i>U</i>. Every countable locally finite group is a subgroup of <i>U</i>. We prove that <i>U</i> is a subgroup of the abstract commensurator of a finite-rank nonabelian free group.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11856-023-2591-8","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
P. Hall constructed a universal countable locally finite group U, determined up to isomorphism by two properties: every finite group C is a subgroup of U, and every embedding of C into U is conjugate in U. Every countable locally finite group is a subgroup of U. We prove that U is a subgroup of the abstract commensurator of a finite-rank nonabelian free group.
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