{"id":"openai-math/a-torsion-free-hyperbolic-group-that-is-not-residually-finite","pdf":"https://github.com/openai/math/blob/main/preprints/a-torsion-free-hyperbolic-group-that-is-not-residually-finite-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/a-torsion-free-hyperbolic-group-that-is-not-residually-finite-September-23-2026","tags":["geometric-group-theory","hyperbolic-groups","residual-finiteness"],"score":0,"title":"A torsion-free hyperbolic group that is not residually finite","domain":"Group theory","family":"252","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.GR","summary":"We construct a torsion-free word-hyperbolic group that is not residually finite, answering the residual-finiteness question for hyperbolic groups negatively.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":2,"published":"2026-09-23","reactions":{},"discussion":[{"url":"https://proofsandprompts.com/2026/10/08/100-reactions-to-100-solutions/#:~:text=it%20looked%20to%20me%20that%20there%20are%20really%20two%20quite%20different%20modules%20in%20the%20proof","date":"2026-10-08","kind":"web","site":"Proofs and Prompts","text":"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…","added":"2026-10-24","title":"100+ reactions to 100+ solutions"},{"url":"https://arxiv.org/abs/2610.24836","date":"2026-10-17","kind":"web","site":"arXiv.org","text":"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.","added":"2026-10-24","title":"An example of a non-sofic hyperbolic group","author":"Harjas Sandhu, Andreas Thom","record":"arxiv/2610.24836"}],"formalized":true,"family_title":"A torsion-free hyperbolic group that is neither residually finite nor linear over any field"}