Progress around the Boone–Higman conjecture
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.
Authors
- Matthew C. B. Zaremsky (ORCID: https://orcid.org/0000-0003-2993-5777)
- Francesco Matucci (ORCID: https://orcid.org/0000-0003-4762-5684)
- Collin Bleak (ORCID: https://orcid.org/0000-0001-5790-1940)
- James Belk (ORCID: https://orcid.org/0000-0002-9392-3378)
Institutions
- University of St Andrews (GB)
- University at Albany, State University of New York (US)
- University of Milano-Bicocca (IT)
- University of Glasgow (GB)
Publication Details
- Journal
- EMS Surveys in Mathematical Sciences
- Published
- 2025-06-16
- DOI
- https://doi.org/10.4171/emss/101
- Primary Topic
- Geometric and Algebraic Topology
- Type
- article
- Field-Weighted Citation Impact
- 0.00