{"title":"性质FW和群的环积:使用Schreier图的一种简单方法","authors":"Paul-Henry Leemann , Grégoire Schneeberger","doi":"10.1016/j.exmath.2022.07.001","DOIUrl":null,"url":null,"abstract":"<div><p>The group property FW stands in-between the celebrated Kazhdan’s property (T) and Serre’s property FA. Among many characterizations, it might be defined, for finitely generated groups, as having all Schreier graphs one-ended.</p><p>It follows from the work of Y. Cornulier that a finitely generated wreath product <span><math><mrow><mi>G</mi><msub><mrow><mo>≀</mo></mrow><mrow><mi>X</mi></mrow></msub><mi>H</mi></mrow></math></span> has property FW if and only if both <span><math><mi>G</mi></math></span> and <span><math><mi>H</mi></math></span> have property FW and <span><math><mi>X</mi></math></span> is finite. The aim of this paper is to give an elementary, direct and explicit proof of this fact using Schreier graphs.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0723086922000391/pdfft?md5=a25144589e5c96c13c5679a9a7e61297&pid=1-s2.0-S0723086922000391-main.pdf","citationCount":"2","resultStr":"{\"title\":\"Property FW and wreath products of groups: A simple approach using Schreier graphs\",\"authors\":\"Paul-Henry Leemann , Grégoire Schneeberger\",\"doi\":\"10.1016/j.exmath.2022.07.001\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The group property FW stands in-between the celebrated Kazhdan’s property (T) and Serre’s property FA. Among many characterizations, it might be defined, for finitely generated groups, as having all Schreier graphs one-ended.</p><p>It follows from the work of Y. Cornulier that a finitely generated wreath product <span><math><mrow><mi>G</mi><msub><mrow><mo>≀</mo></mrow><mrow><mi>X</mi></mrow></msub><mi>H</mi></mrow></math></span> has property FW if and only if both <span><math><mi>G</mi></math></span> and <span><math><mi>H</mi></math></span> have property FW and <span><math><mi>X</mi></math></span> is finite. The aim of this paper is to give an elementary, direct and explicit proof of this fact using Schreier graphs.</p></div>\",\"PeriodicalId\":50458,\"journal\":{\"name\":\"Expositiones Mathematicae\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2022-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0723086922000391/pdfft?md5=a25144589e5c96c13c5679a9a7e61297&pid=1-s2.0-S0723086922000391-main.pdf\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Expositiones Mathematicae\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0723086922000391\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Expositiones Mathematicae","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0723086922000391","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Property FW and wreath products of groups: A simple approach using Schreier graphs
The group property FW stands in-between the celebrated Kazhdan’s property (T) and Serre’s property FA. Among many characterizations, it might be defined, for finitely generated groups, as having all Schreier graphs one-ended.
It follows from the work of Y. Cornulier that a finitely generated wreath product has property FW if and only if both and have property FW and is finite. The aim of this paper is to give an elementary, direct and explicit proof of this fact using Schreier graphs.
期刊介绍：
Our aim is to publish papers of interest to a wide mathematical audience. Our main interest is in expository articles that make high-level research results more widely accessible. In general, material submitted should be at least at the graduate level.Main articles must be written in such a way that a graduate-level research student interested in the topic of the paper can read them profitably. When the topic is quite specialized, or the main focus is a narrow research result, the paper is probably not appropriate for this journal. Most original research articles are not suitable for this journal, unless they have particularly broad appeal.Mathematical notes can be more focused than main articles. These should not simply be short research articles, but should address a mathematical question with reasonably broad appeal. Elementary solutions of elementary problems are typically not appropriate. Neither are overly technical papers, which should best be submitted to a specialized research journal.Clarity of exposition, accuracy of details and the relevance and interest of the subject matter will be the decisive factors in our acceptance of an article for publication. Submitted papers are subject to a quick overview before entering into a more detailed review process. All published papers have been refereed.
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
