{"title":"无限斐波那契群与相对非球面","authors":"M. Edjvet, A. Juhász","doi":"10.1112/tlm3.12007","DOIUrl":null,"url":null,"abstract":"We prove that the generalised Fibonacci group F(r,n) is infinite for (r,n)∈{(7+5k,5),(8+5k,5):k⩾0} . This together with previously known results yields a complete classification of the finite F(r,n) , a problem that has its origins in a question by J. H. Conway in 1965. The method is to show that a related relative presentation is aspherical from which it can be deduced that the groups are infinite.","PeriodicalId":41208,"journal":{"name":"Transactions of the London Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2017-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1112/tlm3.12007","citationCount":"7","resultStr":"{\"title\":\"The infinite Fibonacci groups and relative asphericity\",\"authors\":\"M. Edjvet, A. Juhász\",\"doi\":\"10.1112/tlm3.12007\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove that the generalised Fibonacci group F(r,n) is infinite for (r,n)∈{(7+5k,5),(8+5k,5):k⩾0} . This together with previously known results yields a complete classification of the finite F(r,n) , a problem that has its origins in a question by J. H. Conway in 1965. The method is to show that a related relative presentation is aspherical from which it can be deduced that the groups are infinite.\",\"PeriodicalId\":41208,\"journal\":{\"name\":\"Transactions of the London Mathematical Society\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2017-08-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1112/tlm3.12007\",\"citationCount\":\"7\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Transactions of the London Mathematical Society\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1112/tlm3.12007\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transactions of the London Mathematical Society","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1112/tlm3.12007","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 7
摘要
我们证明广义Fibonacci群F(r,n)对于(r,n)∈{(7+5k,5)，(8+5k,5):k小于0}是无限的。这与先前已知的结果一起产生了有限F(r,n)的完全分类，这个问题起源于1965年J. H. Conway的一个问题。该方法是证明一个相关的相对表示是非球面的，由此可以推导出群是无限的。
The infinite Fibonacci groups and relative asphericity
We prove that the generalised Fibonacci group F(r,n) is infinite for (r,n)∈{(7+5k,5),(8+5k,5):k⩾0} . This together with previously known results yields a complete classification of the finite F(r,n) , a problem that has its origins in a question by J. H. Conway in 1965. The method is to show that a related relative presentation is aspherical from which it can be deduced that the groups are infinite.
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