{"title":"FREE PRODUCT OF TWO ELLIPTIC QUATERNIONIC MÖBIUS TRANSFORMATIONS","authors":"W. Cao","doi":"10.18910/61891","DOIUrl":null,"url":null,"abstract":"Suppose that f and g are two elliptic quaternionic M¨obius transformations of orders m and n respectively. If the hyperbolic distance δ ( f , g ) between fix( f ) and fix( g ) satisfies cosh δ ( f , g ) ≥ cos π m cos π n + 1 sin π m sin π n , then the group (cid:3) f , g (cid:4) is discrete non-elementary and isomorphic to the free product (cid:3) f (cid:4) ∗ (cid:3) g (cid:4) .","PeriodicalId":54660,"journal":{"name":"Osaka Journal of Mathematics","volume":"54 1","pages":"351-362"},"PeriodicalIF":0.5000,"publicationDate":"2017-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Osaka Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.18910/61891","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Suppose that f and g are two elliptic quaternionic M¨obius transformations of orders m and n respectively. If the hyperbolic distance δ ( f , g ) between fix( f ) and fix( g ) satisfies cosh δ ( f , g ) ≥ cos π m cos π n + 1 sin π m sin π n , then the group (cid:3) f , g (cid:4) is discrete non-elementary and isomorphic to the free product (cid:3) f (cid:4) ∗ (cid:3) g (cid:4) .
期刊介绍：
Osaka Journal of Mathematics is published quarterly by the joint editorship of the Department of Mathematics, Graduate School of Science, Osaka University, and the Department of Mathematics, Faculty of Science, Osaka City University and the Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University with the cooperation of the Department of Mathematical Sciences, Faculty of Engineering Science, Osaka University. The Journal is devoted entirely to the publication of original works in pure and applied mathematics.
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