JournalsggdVol. 12, No. 3pp. 1061–1068

On self-similarity of wreath products of abelian groups

  • Alex C. Dantas

    Universidade Tecnológica Federal do Paraná, Guarapuava, Brazil
  • Said N. Sidki

    Universidade de Brasilia, Brazil
On self-similarity of wreath products of abelian groups cover
Download PDF

A subscription is required to access this article.

Abstract

We prove that in a self-similar wreath product of abelian groups G=BG=B wr XX, if XX is torsion-free then BB is torsion of finite exponent. Therefore, in particular, the group Z\mathbb{Z} wr Z\mathbb{Z} cannot be self-similar. Furthemore, we prove that if LL is a self-similar abelian group then LωL^{\omega} wr C2C_2 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. 1061–1068

DOI 10.4171/GGD/462