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# Assouad-Nagata Dimension of Wreath Products of Groups

Published:2013-08-10
Printed: Jun 2014
• N. Brodskiy,
Department of Mathematics, University of Tennessee, 227 Ayres Hall, 1403 Circle Drive, Knoxville, TN 37996
• J. Dydak,
Department of Mathematics, University of Tennessee, 227 Ayres Hall, 1403 Circle Drive, Knoxville, TN 37996
• U. Lang,
Eidgen Technische Hochschule Zentrum, CH-8092 Zürich, Switzerland
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## Abstract

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 $\dim_{AN}(H\wr G)$ of $H\wr G$ depends on the growth of $G$ as follows: \par If the growth of $G$ is not bounded by a linear function, then $\dim_{AN}(H\wr G)=\infty$, otherwise $\dim_{AN}(H\wr G)=\dim_{AN}(G)\leq 1$.
 Keywords: Assouad-Nagata dimension, asymptotic dimension, wreath product, growth of groups
 MSC Classifications: 54F45 - Dimension theory [See also 55M10] 55M10 - Dimension theory [See also 54F45] 54C65 - Selections [See also 28B20]

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