{"id":"openai-math/An-infinite-finitely-presented-periodic-group","pdf":"https://github.com/openai/math/blob/main/preprints/An-infinite-finitely-presented-periodic-group-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/An-infinite-finitely-presented-periodic-group-September-23-2026","tags":["group-theory","burnside-problem"],"score":0,"title":"An infinite finitely presented periodic group","domain":"Group theory","family":"247","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.GR","summary":"We construct an infinite group with an ordinary finite presentation in which every element has finite order, answering the finitely presented Burnside question negatively. We also construct an infinite-dimensional finitely presented nonunital nil associative algebra over 𝔽 2 that is Jacobson radical but not nilpotent. Its unitization is finitely presented, algebraic, and infinite-dimensional. These algebras answer the finitely presented nil- and radical-algebra nilpotence questions and the finite-presentation version of Kurosh's algebraic finiteness question negatively.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-23","reactions":{},"formalized":false,"family_title":"An infinite finitely presented residually finite 2-group and a finitely presented nil algebra"}