Assouad-Nagata dimension of wreath products of groups

Details Assouad-Nagata dimension of wreath products of groups Assouad-Nagata dimension of wreath products of groups

2006-11-11

arxiv.org/abs/math/0611331v2

Mathematics

Metric Geometry

11 pages, new references added

Scientific paper

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: If the growth of $G$
is not bounded by a linear function, then $\dim_{AN}(H\wr G)=\infty$, otherwise
$\dim_{AN}(H\wr G)=\dim_{AN}(G)\leq 1$.

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