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Assouad–Nagata Dimension of Wreath Products of Groups

Published online by Cambridge University Press:  20 November 2018

N. Brodskiy ,
J. Dydak  and
U. Lang
N. Brodskiy
Affiliation:
Department of Mathematics, University of Tennessee, Knoxville, TN 37996, USA e-mail: brodskiy@math.utk.edudydak@math.utk.edu
J. Dydak
Affiliation:
Department of Mathematics, University of Tennessee, Knoxville, TN 37996, USA e-mail: brodskiy@math.utk.edudydak@math.utk.edu
U. Lang
Affiliation:
Eidgen Technische Hochschule Zentrum, CH-8092 Zürich, Switzerland lang@math.ethz.ch
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Abstract

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Consider the wreath product $H\,\wr \,G$, where $H\,\ne \,1$ is finite and $G$ is finitely generated. We show that the Assouad–Nagata dimension ${{\dim}_{AN}}\left( H\,\wr \,G \right)$ of $H\,\wr \,G$ depends on the growth of $G$ as follows: if the growth of $G$ is not bounded by a linear function, then ${{\dim}_{AN}}\left( H\,\wr \,G \right)\,=\,\infty$; otherwise ${{\dim}_{AN}}\left( H\,\wr \,G \right)\,=\,{{\dim}_{AN}}\left( G \right)\,\le \,1$.

Keywords

54F4555M1054C65Assouad–Nagata dimensionasymptotic dimensionwreath productgrowth of groups
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 57 , Issue 2 , 14 June 2014 , pp. 245 - 253
Copyright
Copyright © Canadian Mathematical Society 2014

Footnotes

The second-named author was partially supported by the Center for Advanced Studies in Mathematics at Ben Gurion University of the Negev (Beer-Sheva, Israel).

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