{"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}
引用次数: 7
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.
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。
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
