Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 247-02. An infinite finitely presented periodic group
Manuscript map · lines 7305–7314
OpenAI@2026-10-07#rem:oai-p-247-02
Authors: OpenAI. Family 247.
Title: An infinite finitely presented periodic group.
Abstract: 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 𝔽2 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.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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