Progress around the Boone–Higman conjecture

James Belk; Collin Bleak; Francesco Matucci; Matthew C. B. Zaremsky

doi:10.4171/emss/101

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Progress around the Boone–Higman conjecture

James Belk
University of Glasgow, Glasgow, UK
Collin Bleak
University of St Andrews, St Andrews, UK
Francesco Matucci
Università degli Studi di Milano–Bicocca, Milan, Italy
- MathSciNet
- ORCID
Matthew C. B. Zaremsky
University at Albany (SUNY), Albany, USA
- MathSciNet
- ORCID

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Abstract

A conjecture of Boone and Higman from the 1970’s asserts that a finitely generated group $G$ has solvable word problem if and only if $G$ can be embedded into a finitely presented simple group. We comment on the history of this conjecture and survey recent results that establish the conjecture for many large classes of interesting groups.

Cite this article

James Belk, Collin Bleak, Francesco Matucci, Matthew C. B. Zaremsky, Progress around the Boone–Higman conjecture. EMS Surv. Math. Sci. (2025), published online first

DOI 10.4171/EMSS/101