Preprint in the OpenAI Math release

A universal group of type F∞

OpenAI

Abstract

We construct a single group of type F $_{\infty}$ containing every finitely presented group. Its finitely generated subgroups, up to isomorphism, are exactly the finitely generated recursively presented groups. This answers the F $_{\infty}$ form of the higher-dimensional Higman embedding question.

open until 1 Jan 2028

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

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