{"title":"Failure of the finitely generated intersection property for ascending HNN extensions of free groups","authors":"Jacob Bamberger, D. Wise","doi":"10.1142/s0218196722500370","DOIUrl":null,"url":null,"abstract":"The main result in this paper is the failure of the finitely generated intersection property (FGIP) of ascending HNN extensions of non-cyclic finite rank free groups. This class of groups consists of free-by-cyclic groups and properly ascending HNN extensions of free groups. We also give a sufficient condition for the failure of the FGIP in the context of relative hyperbolicity, we apply this to free-by-cyclic groups of exponential growth.","PeriodicalId":13615,"journal":{"name":"Int. J. Algebra Comput.","volume":"1 1","pages":"885-893"},"PeriodicalIF":0.0000,"publicationDate":"2022-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Int. J. Algebra Comput.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s0218196722500370","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
The main result in this paper is the failure of the finitely generated intersection property (FGIP) of ascending HNN extensions of non-cyclic finite rank free groups. This class of groups consists of free-by-cyclic groups and properly ascending HNN extensions of free groups. We also give a sufficient condition for the failure of the FGIP in the context of relative hyperbolicity, we apply this to free-by-cyclic groups of exponential growth.
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