Progress around the Boone-Higman conjecture

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

Research output: Working paperPreprint


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.
Original languageEnglish
Number of pages21
Publication statusPublished - 28 Jun 2023


  • Group theory


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