OpenAI · 247-01 · 2026-10-05 · Group theory

An infinite finitely presented residually finite 2-group

preprints/An-infinite-finitely-presented-residually-finite-2-group-October-5-2026

Family 247. An infinite finitely presented residually finite $2$ -group.

The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.

Read against the standing problems

Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N

Constructs an infinite finitely presented residually finite group whose elements all have finite $2$ -power order, answering the finitely presented Burnside problem negatively even in this class. The construction also yields an infinite-dimensional finitely presented nil associative $F_{2}$ -algebra and a finitely presented infinite-dimensional algebraic unitization, giving negative answers to the corresponding nilpotence and Kurosh finiteness questions.

We prove that the infinite, ordinarily finitely presented periodic Steinberg group $Γ = St_{12} (R)$ of a companion paper is residually finite. Its finite-index subgroup $G = ker (Γ \to St_{12} (F_{2}))$ is infinite, ordinarily finitely presented, and residually finite, and every element of G has finite 2-power order. The orders of its elements are unbounded. Phases of long words in the companion's graded algebra allow finite degree truncations to detect all elements of Γ, including the central kernel.

Preprint source and Lean scope

The abstract above is the catalogue abstract. The sections below are the full preprint source, 0 sections. This page is not only the abstract. The manuscript file is loading.

A Lean scope note is stored for family 247, but it does not name this preprint. It names 247-02. This page still has the full preprint source. No compilation is asserted. O.1 stays NOT_CLOSED.