{"title":"关于自由群中闭子集的积","authors":"Rita Gitik, E. Rips","doi":"10.1515/9783110638387-009","DOIUrl":null,"url":null,"abstract":"We present examples of closed subsets of a free group such that their product is not closed in the profinite topology. We discuss how to characterize a subset of a free group which is closed in the profinite topology and its product with any finitely generated subgroup of a free group is also closed in the profinite topology.","PeriodicalId":428206,"journal":{"name":"Elementary Theory of Groups and Group Rings, and Related Topics","volume":"7 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On products of closed subsets in free groups\",\"authors\":\"Rita Gitik, E. Rips\",\"doi\":\"10.1515/9783110638387-009\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We present examples of closed subsets of a free group such that their product is not closed in the profinite topology. We discuss how to characterize a subset of a free group which is closed in the profinite topology and its product with any finitely generated subgroup of a free group is also closed in the profinite topology.\",\"PeriodicalId\":428206,\"journal\":{\"name\":\"Elementary Theory of Groups and Group Rings, and Related Topics\",\"volume\":\"7 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-06-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Elementary Theory of Groups and Group Rings, and Related Topics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/9783110638387-009\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Elementary Theory of Groups and Group Rings, and Related Topics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/9783110638387-009","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We present examples of closed subsets of a free group such that their product is not closed in the profinite topology. We discuss how to characterize a subset of a free group which is closed in the profinite topology and its product with any finitely generated subgroup of a free group is also closed in the profinite topology.
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