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A torsion-free hyperbolic group that is not residually finite

OpenAI

OpenAI Mathopenai-math/a-torsion-free-hyperbolic-group-that-is-not-residually-finiteSep 23, 2026math.GRAI-generatedscore 0 · 🔥 2 posts

We construct a torsion-free word-hyperbolic group that is not residually finite, answering the residual-finiteness question for hyperbolic groups negatively.

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100+ reactions to 100+ solutionsProofs and PromptsOct 8, 2026

it looked to me that there are really two quite different modules in the proof. One purely algebraic and the other geometric. After fiddling around with Astra for some time today, it gave me a reasonable sounding purely group-ring theoretic criterion for non-residual finiteness of a group. It…

An example of a non-sofic hyperbolic grouparXiv.orgHarjas Sandhu, Andreas ThomOct 17, 2026in the index

We construct a torsion-free, two-dimensional, word-hyperbolic group which is not sofic. Our construction builds on OpenAI's construction of a non-residually finite hyperbolic group, see OpenAI 252.

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