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

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Abstract | References | Similar Articles | Additional Information

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

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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

DOI:
http://dx.doi.org/10.1090/S0002-9939-07-08970-8

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.