On quasi-isometric embeddings of lamplighter groups

被引：1

作者：

Inamdar, S. P. ^{[1
]}

Naolekar, Aniruddha C. ^{[1
]}

机构：

[1] Indian Stat Inst, Dept Theoret Stat & Math, Bangalore Ctr, Bangalore 560059, Karnataka, India

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2007年 / 135卷 / 12期

关键词：

Geometric group theory; Lamplighter groups;

D O I：

10.1090/S0002-9939-07-08970-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We denote by Gamma(G) the Lamplighter group of a finite group G. In this article, we show that if G and H are two finite groups with at least two elements, then there exists a quasi-isometric embedding from Gamma(G) to Gamma(H). We also prove that the quasi-isometry group QI(Gamma(G)) of Gamma(G) contains all finite groups. We then show that the group of automorphisms of Gamma(Zn) has infinite index in QI(Gamma(Zn)).

引用

页码：3789 / 3794

页数：6

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