Boone–Higman embeddings for contracting self-similar groups
James Belk
University of Glasgow, Glasgow, UKFrancesco Matucci
Università degli Studi di Milano–Bicocca, Milan, Italy

Abstract
We give a short proof that every contracting self-similar group embeds into a finitely presented simple group. In particular, any contracting self-similar group embeds into the corresponding Röver–Nekrashevych group, and this in turn embeds into one of the twisted Brin–Thompson groups introduced by the first author and Matthew Zaremsky. The proof here is a simplification of a more general argument given by the authors, Collin Bleak and Matthew Zaremsky, for contracting rational similarity groups.
Cite this article
James Belk, Francesco Matucci, Boone–Higman embeddings for contracting self-similar groups. Groups Geom. Dyn. (2025), published online first
DOI 10.4171/GGD/898