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arXiv · 2212.07165

Realizing residually finite groups as subgroups of branch groups

Steffen Kionke·Eduard Schesler
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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.

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Steffen Kionke, Eduard Schesler. 2022-12-14. Realizing residually finite groups as subgroups of branch groups. https://doi.org/10.1112/blms.12948

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