{"id":"openai-math/A-universal-group-of-type-F-infinity","pdf":"https://github.com/openai/math/blob/main/preprints/A-universal-group-of-type-F-infinity-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/A-universal-group-of-type-F-infinity-September-23-2026","tags":["geometric-group-theory","finiteness-properties","embedding-theorems"],"score":0,"title":"A universal group of type F∞","domain":"Group theory","family":"250","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.GR","summary":"We construct a single group of type F ∞ containing every finitely presented group. Its finitely generated subgroups, up to isomorphism, are exactly the finitely generated recursively presented groups. This answers the F ∞ form of the higher-dimensional Higman embedding question.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-23","reactions":{},"formalized":true,"family_title":"Boone–Higman embeddings with higher finiteness"}