Assouad-Nagata dimension of wreath products of groups

Brodskiy, N.; Dydak, J.; Lang, U.

Assouad-Nagata dimension of wreath products of groups

Authors

Brodskiy, N.

Dydak, J.

Lang, U.

Description

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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