On quasi-isometric embeddings of Lamplighter groups
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- by S. P. Inamdar and Aniruddha C. Naolekar PDF
- Proc. Amer. Math. Soc. 135 (2007), 3789-3794 Request permission
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
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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
- 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
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 3789-3794
- MSC (2000): Primary 20F65; Secondary 20F28
- DOI: https://doi.org/10.1090/S0002-9939-07-08970-8
- MathSciNet review: 2341928