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We prove that in a self-similar wreath product of abelian groups wr , if is torsion-free then is torsion of finite exponent. Therefore, in particular, the group wr cannot be self-similar. Furthemore, we prove that if is a self-similar abelian group then wr is also self-similar.
Cite this article
Alex C. Dantas, Said N. Sidki, On self-similarity of wreath products of abelian groups. Groups Geom. Dyn. 12 (2018), no. 3, pp. 1061–1068DOI 10.4171/GGD/462