Realizing residually finite groups as subgroups of branch groups

Abstract

We prove that every finitely generated, residually finite group $G$ embeds into a finitely generated perfect branch group $\Gamma$ such that many properties of $G$ are preserved under this embedding. Among those are the properties of being torsion, being amenable, and not containing a non-abelian free group. As an application we construct a finitely generated, non-amenable torsion branch group.

12 pages. Comments welcome!

References in corpus (1)

• Extensions of amenable groups by recurrent groupoids