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arXiv · 1610.08994

On self-similarity of wreath products of abelian groups

Alex C. Dantas·Said N. Sidki
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Abstract

We prove that a self-similar free abelian group has finite rank. We apply the result to self-similar wreath products of abelian groups $G=BwrX$. We show that if $X$ is torsion-free, then $B$ is torsion of finite exponent. Furthemore, we construct a self-similar group $G=BwrC_{2}$ where $B$ is free abelian of infinite rank.

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Alex C. Dantas, Said N. Sidki. 2016-10-27. On self-similarity of wreath products of abelian groups. https://arxiv.org/abs/1610.08994

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