What was already known
Baumslag asked whether one-relator groups with commutator relators have these properties. Olshanskii had already given negative residual-finiteness and automaticity examples for the broader condition that the relator lies in [F,F].
AI involvement
Wang and Zhang credit ChatGPT with assisting in construction of the example family. They supplied the retract, epimorphism and Dehn-function arguments, checked all proofs and edited the paper.
ChatGPT is credited with constructing the example family on which the negative answers depend; the human authors supplied the proofs.
Importance
Answers the three questions for the narrower literal-commutator case with one explicit family.
Limitations
The authors checked the proofs, but the precise model prompts and its share in selecting the parameterized relator are undisclosed.
Technical verification
Both authors explicitly report checking all arguments in the final paper; this is source-reported human verification.
Independent checking
Checking all arguments and editing the paper
- Checker
- Ke Wang and Qiang Zhang, authors
- Scope
- Theorem 1.3 for G_m and its three consequences
- Basis
- Reported by the linked checker
Human understanding
The authors explain the Baumslag–Solitar retract, noninjective epimorphism and non-quadratic Dehn-function obstruction.
Correction and publication history
Answers the three questions for the narrower literal-commutator case with one explicit family.
Read this published revision