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An infinite finitely presented periodic group

Source: github.com/openai/math/tree/main/preprints/An-infinite-fini…

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OpenAI Mathopenai-math/An-infinite-finitely-presented-periodic-groupSep 23, 2026math.GRAI-generatedscore 0

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.

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