A Torsion-Free Group Algebra That Is Not Directly Finite
Source: github.com/openai/math/tree/main/preprints/A-Torsion-Free-G…
We construct a finitely presented torsion-free counterexample to Kaplansky's direct finiteness conjecture over the field of two elements. The group admits a finite two-dimensional classifying complex.
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100+ reactions to 100+ solutionsProofs and PromptsJohan ÖinertOct 8, 2026
Later, in “A Torsion-Free Group Algebra That Is Not Directly Finite” (dated October 4), OpenAI claims to have found a counterexample to Kaplansky’s direct finiteness conjecture for group algebras over the field with two elements. It follows trivially that the latter document provides a…