On self-similarity of wreath products of abelian groups

2016/10/27 by Dantas, Alex C., Sidki, Said N. · 1 citation
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1610.08994

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=BwrC₂ where B is free abelian of infinite rank.

Cited by

• Non self-similar metabelian groups

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