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Progress around the Boone–Higman conjecture

  • James Belk

    University of Glasgow, Glasgow, UK
    ORCID

  • Collin Bleak

    University of St Andrews, St Andrews, UK
    ORCID

  • Francesco Matucci

    Università degli Studi di Milano–Bicocca, Milan, Italy
    ORCID

  • Matthew C. B. Zaremsky

    University at Albany (SUNY), Albany, USA
    ORCID
Progress around the Boone–Higman conjecture cover

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Abstract

A conjecture of Boone and Higman from the 1970’s asserts that a finitely generated group has solvable word problem if and only if 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