Realising residually finite groups as subgroups of branch groups.

We prove that every finitely generated, residually finite group G$G$ embeds into a finitely generated perfect branch group Γ$\Gamma$ such that many properties of G$G$ 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. [ABSTRACT FROM AUTHOR]