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Assouad-Nagata dimension of nilpotent groups with arbitrary left invariant metrics


Author: J. Higes
Journal: Proc. Amer. Math. Soc. 138 (2010), 2235-2244
MSC (2000): Primary 54F45; Secondary 55M10, 54C65
DOI: https://doi.org/10.1090/S0002-9939-10-10240-8
Published electronically: February 12, 2010
MathSciNet review: 2596064
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Abstract: Suppose $ G$ is a countable, not necessarily finitely generated, group. We show $ G$ admits a proper, left invariant metric $ d_G$ such that the Assouad-Nagata dimension of $ (G,d_G)$ is infinite, provided the center of $ G$ is not locally finite. As a corollary we solve two problems of A. Dranishnikov.


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Additional Information

J. Higes
Affiliation: Departamento de Geometría y Topología, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, Madrid, 28040, Spain
Email: josemhiges@yahoo.es

DOI: https://doi.org/10.1090/S0002-9939-10-10240-8
Keywords: Assouad-Nagata dimension, asymptotic dimension, nilpotent groups
Received by editor(s): June 11, 2009
Received by editor(s) in revised form: October 3, 2009
Published electronically: February 12, 2010
Additional Notes: The author is supported by Grant AP2004-2494 from the Ministerio de Educación y Ciencia, Spain, and project MEC, MTM2006-0825. He also thanks Jerzy Dydak and N. Brodskyi for helpful comments and support.
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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