{"title":"(1)、(2)、(3)和(4)","authors":"Azer Akhmedov","doi":"10.1017/s0017089524000181","DOIUrl":null,"url":null,"abstract":"We prove the <jats:italic>Girth Alternative</jats:italic> for finitely generated subgroups of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0017089524000181_inline2.png\"/> <jats:tex-math> $PL_o(I)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>. We also prove that a finitely generated subgroup of <jats:italic>Homeo</jats:italic><jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0017089524000181_inline3.png\"/> <jats:tex-math> $_{+}(I)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> which is sufficiently rich with hyperbolic-like elements has infinite girth.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Girth Alternative for subgroups of\",\"authors\":\"Azer Akhmedov\",\"doi\":\"10.1017/s0017089524000181\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove the <jats:italic>Girth Alternative</jats:italic> for finitely generated subgroups of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" mime-subtype=\\\"png\\\" xlink:href=\\\"S0017089524000181_inline2.png\\\"/> <jats:tex-math> $PL_o(I)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>. We also prove that a finitely generated subgroup of <jats:italic>Homeo</jats:italic><jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" mime-subtype=\\\"png\\\" xlink:href=\\\"S0017089524000181_inline3.png\\\"/> <jats:tex-math> $_{+}(I)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> which is sufficiently rich with hyperbolic-like elements has infinite girth.\",\"PeriodicalId\":50417,\"journal\":{\"name\":\"Glasgow Mathematical Journal\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-05-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Glasgow Mathematical Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1017/s0017089524000181\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Glasgow Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/s0017089524000181","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
We prove the Girth Alternative for finitely generated subgroups of $PL_o(I)$ . We also prove that a finitely generated subgroup of Homeo $_{+}(I)$ which is sufficiently rich with hyperbolic-like elements has infinite girth.
期刊介绍：
Glasgow Mathematical Journal publishes original research papers in any branch of pure and applied mathematics. An international journal, its policy is to feature a wide variety of research areas, which in recent issues have included ring theory, group theory, functional analysis, combinatorics, differential equations, differential geometry, number theory, algebraic topology, and the application of such methods in applied mathematics.
The journal has a web-based submission system for articles. For details of how to to upload your paper see GMJ - Online Submission Guidelines or go directly to the submission site.
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