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A torsion-free direct-finiteness counterexample

Characteristic-zero and sofic-group direct-finiteness theorems do not settle arbitrary positive-characteristic group algebras.

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Understanding the problem

Read the background

Characteristic-zero and sofic-group direct-finiteness theorems do not settle arbitrary positive-characteristic group algebras. The target is failure of the reverse inverse identity under the stated restrictions.

This entry covers the torsion-free two-element-field construction. Other characteristic, determinant, or cellular-automaton companions are not separate records here.

Why it matters

If correct, refutes the stated positive-characteristic direct-finiteness target even for a torsion-free finitely presented group.

What counts as progress

A sourced resolution or substantial advance on the precise target, with hypotheses, prior context, and verification evidence stated separately.

What to watch for

  • Assess the precise statement and assumptions before comparing results.
  • This entry covers the torsion-free two-element-field construction. Other characteristic, determinant, or cellular-automaton companions are not separate records here.
  • Track independent assessments, dependencies, corrections, and withdrawals separately from importance.

Background review: 2026-10-11. Selected sources:

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