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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 Assouad-Nagata dimension, asymptotic dimension, wreath product, growth of groups
MSC Classifications: 54F45, 55M10, 54C65 show english descriptions Dimension theory [See also 55M10]
Dimension theory [See also 54F45]
Selections [See also 28B20]
54F45 - Dimension theory [See also 55M10]
55M10 - Dimension theory [See also 54F45]
54C65 - Selections [See also 28B20]
 

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