{"title":"算术试探性双曲晶格并非局部扩展残差有限","authors":"Nikolay Bogachev, Leone Slavich, Hongbin Sun","doi":"10.1093/imrn/rnae053","DOIUrl":null,"url":null,"abstract":"A group is LERF (locally extended residually finite) if all its finitely generated subgroups are separable. We prove that the trialitarian arithmetic lattices in $\\mathbf{PSO}_{7,1}(\\mathbb{R})$ are not LERF. This result, together with previous work by the third author, implies that no arithmetic lattice in $\\mathbf{PO}_{n,1}(\\mathbb{R})$, $n>3$, is LERF.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Arithmetic Trialitarian Hyperbolic Lattices Are Not Locally Extended Residually Finite\",\"authors\":\"Nikolay Bogachev, Leone Slavich, Hongbin Sun\",\"doi\":\"10.1093/imrn/rnae053\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A group is LERF (locally extended residually finite) if all its finitely generated subgroups are separable. We prove that the trialitarian arithmetic lattices in $\\\\mathbf{PSO}_{7,1}(\\\\mathbb{R})$ are not LERF. This result, together with previous work by the third author, implies that no arithmetic lattice in $\\\\mathbf{PO}_{n,1}(\\\\mathbb{R})$, $n>3$, is LERF.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-04-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1093/imrn/rnae053\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1093/imrn/rnae053","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Arithmetic Trialitarian Hyperbolic Lattices Are Not Locally Extended Residually Finite
A group is LERF (locally extended residually finite) if all its finitely generated subgroups are separable. We prove that the trialitarian arithmetic lattices in $\mathbf{PSO}_{7,1}(\mathbb{R})$ are not LERF. This result, together with previous work by the third author, implies that no arithmetic lattice in $\mathbf{PO}_{n,1}(\mathbb{R})$, $n>3$, is LERF.
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