Preprint in the OpenAI Math release

Simple F∞ overgroups of groups with decidable word problem

OpenAI

Abstract

Every finitely generated group with decidable word problem embeds in a simple group of type F $_{\infty}$ . This resolves the higher-finiteness strengthening of the Boone–Higman conjecture.

open until 1 Jan 2028

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

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

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