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# Assouad-Nagata dimension of wreath products of groups

Published:2013-08-10

• 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