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Preprint in the OpenAI Math release

Finite algebraic envelopes and the Boone–Higman conjecture

OpenAI

Abstract

We prove the Boone–Higman conjecture. A finitely generated group has decidable word problem if and only if it embeds in a finitely presented simple group.

open until 1 Jan 2028

est. 50% chance this result is independently verified by the end of 2027.

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