Geodesic
Assouad–Nagata Dimension of Wreath Products of Groups
Canadian mathematical bulletin, Tome 57 (2014) no. 2, pp. 245-253

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DOI

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 ${{\dim}_{AN}}\left( H\,\wr \,G \right)\,=\,{{\dim}_{AN}}\left( G \right)\,\le \,1$ .
DOI : 10.4153/CMB-2013-024-8
Mots-clés : 54F45, 55M10, 54C65, Assouad–Nagata dimension, asymptotic dimension, wreath product, growth of groups 
Brodskiy, N.; Dydak, J.; Lang, U. Assouad–Nagata Dimension of Wreath Products of Groups. Canadian mathematical bulletin, Tome 57 (2014) no. 2, pp. 245-253. doi: 10.4153/CMB-2013-024-8
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     title = {Assouad{\textendash}Nagata {Dimension} of {Wreath} {Products} of {Groups}},
     journal = {Canadian mathematical bulletin},
     pages = {245--253},
     year = {2014},
     volume = {57},
     number = {2},
     doi = {10.4153/CMB-2013-024-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2013-024-8/}
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