Group theory·OpenAI Math·Result 252·Lean formalisation listed
A torsion-free hyperbolic group that is neither residually finite nor linear over any field
One of the 372 results in OpenAI's public mathematics catalogue, filed under group theory: 1 preprint, the latest dated 23 September 2026. This page quotes OpenAI's own summary of the claim, links the paper and abstract, and will embed the animation.
Latest paper
A torsion-free hyperbolic group that is not residually finite
The animation for this result has not been released yet. Subscribe on YouTube to catch it.
What OpenAI claims
Constructs a torsion-free word-hyperbolic group that is not residually finite, answering the residual-finiteness question negatively. One fixed nonidentity element is killed by every finite-dimensional linear representation over every commutative field, so the group is not linear over any such field. (Lean)
Paper
A torsion-free hyperbolic group that is not residually finite
We construct a torsion-free word-hyperbolic group that is not residually finite, answering the residual-finiteness question for hyperbolic groups negatively.
Status
Preprint. The paper has not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.
Related results in Group theory
- 253An infinite finitely presented simple amenable groupLean
- 254Classifying spaces and geometric obstructions for Artin groupsLean
- 255Quasi-isometric recognition of virtually polycyclic groupsLean
- 256Nonsingular systems of equations over arbitrary groupsLean
- 257A hyperbolic group without a geometric CAT(0) actionLean
- 258Gersten’s conjecture and virtual compact specialness of one-relator groups
