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.
Belk, J., Bleak, C., Matucci, F., Zaremsky, M. (2025). Progress around the Boone-Higman conjecture. EMS SURVEYS IN MATHEMATICAL SCIENCES [10.4171/emss/101].
Progress around the Boone-Higman conjecture
Matucci, F;
2025
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.
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