{"title":"虚拟辫子和排列","authors":"P. Bellingeri, L. Paris","doi":"10.5802/aif.3336","DOIUrl":null,"url":null,"abstract":"Let VB_n be the virtual braid group on n strands and let S_n be the symmetric group on n letters. Let n, m ∈ N such that n ≥ 5, m ≥ 2 and n ≥ m. We determine all possible homomorphisms from VB_n to S_m , from S_n to VB_m and from VB_n to VB_m. As corollaries we get that Out(VB_n) is isomorphic to the Klein group and that VB_n is both Hopfian and co-Hofpian.","PeriodicalId":8427,"journal":{"name":"arXiv: Group Theory","volume":"2 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2018-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"8","resultStr":"{\"title\":\"Virtual braids and permutations\",\"authors\":\"P. Bellingeri, L. Paris\",\"doi\":\"10.5802/aif.3336\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let VB_n be the virtual braid group on n strands and let S_n be the symmetric group on n letters. Let n, m ∈ N such that n ≥ 5, m ≥ 2 and n ≥ m. We determine all possible homomorphisms from VB_n to S_m , from S_n to VB_m and from VB_n to VB_m. As corollaries we get that Out(VB_n) is isomorphic to the Klein group and that VB_n is both Hopfian and co-Hofpian.\",\"PeriodicalId\":8427,\"journal\":{\"name\":\"arXiv: Group Theory\",\"volume\":\"2 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-08-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"8\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Group Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5802/aif.3336\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Group Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5802/aif.3336","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Let VB_n be the virtual braid group on n strands and let S_n be the symmetric group on n letters. Let n, m ∈ N such that n ≥ 5, m ≥ 2 and n ≥ m. We determine all possible homomorphisms from VB_n to S_m , from S_n to VB_m and from VB_n to VB_m. As corollaries we get that Out(VB_n) is isomorphic to the Klein group and that VB_n is both Hopfian and co-Hofpian.
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