{"title":"有循环边群的群的无参数图","authors":"Andrei Jaikin-Zapirain, Ismael Morales","doi":"10.1112/jlms.12937","DOIUrl":null,"url":null,"abstract":"<p>We establish a combination theorem for parafree groups. These groups were introduced by Baumslag in the sixties. One of the current motivations for a better understanding of their structure is that they show up naturally in connection with Remeslennikov's conjecture on the profinite rigidity of free groups. In this article, we determine when the fundamental group of a finite graph of groups with cyclic edge groups is parafree.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"109 6","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2024-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12937","citationCount":"0","resultStr":"{\"title\":\"Parafree graphs of groups with cyclic edge groups\",\"authors\":\"Andrei Jaikin-Zapirain, Ismael Morales\",\"doi\":\"10.1112/jlms.12937\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We establish a combination theorem for parafree groups. These groups were introduced by Baumslag in the sixties. One of the current motivations for a better understanding of their structure is that they show up naturally in connection with Remeslennikov's conjecture on the profinite rigidity of free groups. In this article, we determine when the fundamental group of a finite graph of groups with cyclic edge groups is parafree.</p>\",\"PeriodicalId\":49989,\"journal\":{\"name\":\"Journal of the London Mathematical Society-Second Series\",\"volume\":\"109 6\",\"pages\":\"\"},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2024-05-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12937\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the London Mathematical Society-Second Series\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/jlms.12937\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the London Mathematical Society-Second Series","FirstCategoryId":"100","ListUrlMain":"https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/jlms.12937","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
We establish a combination theorem for parafree groups. These groups were introduced by Baumslag in the sixties. One of the current motivations for a better understanding of their structure is that they show up naturally in connection with Remeslennikov's conjecture on the profinite rigidity of free groups. In this article, we determine when the fundamental group of a finite graph of groups with cyclic edge groups is parafree.
期刊介绍：
The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.
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