Compression bounds for wreath products

Li, Sean

doi:10.1090/S0002-9939-10-10307-4

Compression bounds for wreath products
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Proc. Amer. Math. Soc. 138 (2010), 2701-2714 Request permission

Abstract:

We show that if $G$ and $H$ are finitely generated groups whose Hilbert compression exponent is positive, then so is the Hilbert compression exponent of the wreath product $G \wr H$. We also prove an analogous result for coarse embeddings of wreath products. In the special case $G=\mathbb {Z}$, $H=\mathbb {Z} \wr \mathbb {Z}$ our result implies that the Hilbert compression exponent of $\mathbb {Z}\wr (\mathbb {Z}\wr \mathbb {Z})$ is at least $1/4$, answering a question posed by several authors.

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