Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On quasi-isometric embeddings of Lamplighter groups


Authors: S. P. Inamdar and Aniruddha C. Naolekar
Journal: Proc. Amer. Math. Soc. 135 (2007), 3789-3794
MSC (2000): Primary 20F65; Secondary 20F28
Published electronically: September 7, 2007
MathSciNet review: 2341928
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: 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 $ {\mathcal Q}I(\Gamma_G)$ of $ \Gamma_G$ contains all finite groups. We then show that the group of automorphisms of $ \Gamma_{{\mathbb{Z}}_n}$ has infinite index in $ {\mathcal Q}I(\Gamma_{{\mathbb{Z}}_n})$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 20F65, 20F28

Retrieve articles in all journals with MSC (2000): 20F65, 20F28


Additional Information

S. P. Inamdar
Affiliation: Department of Theoretical Statistics and Mathematics, Indian Statistical Institute, Bangalore Centre, 8th Mile, Mysore Road, Bangalore, India 560059
Email: inamdar@ns.isibang.ac.in

Aniruddha C. Naolekar
Affiliation: Department of Theoretical Statistics and Mathematics, Indian Statistical Institute, Bangalore Centre, 8th Mile, Mysore Road, Bangalore, India 560059
Email: ani@ns.isibang.ac.in

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08970-8
PII: S 0002-9939(07)08970-8
Keywords: Lamplighter groups, geometric group theory
Received by editor(s): May 11, 2006
Received by editor(s) in revised form: September 12, 2006, and September 21, 2006
Published electronically: September 7, 2007
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.