Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 247-01. An infinite finitely presented residually finite 2-group
Manuscript map · lines 7295–7304
OpenAI@2026-10-07#rem:oai-p-247-01
Authors: OpenAI. Family 247.
Title: An infinite finitely presented residually finite 2-group.
Abstract: We prove that the infinite, ordinarily finitely presented periodic Steinberg group ${}Gamma={}mathop{{}mathrm{St}}{}nolimits _{12}(R)$ of a companion paper is residually finite. Its finite-index subgroup $G={}ker({}Gamma{}to{}mathop{{}mathrm{St}}{}nolimits _{12}({}mathbb F_2))$ 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.
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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