Commutator Relators Do Not Force Hopficity, Residual Finiteness or Automaticity
Baumslag asked whether a one-relator group with a commutator is Hopfian, residually finite or automatic. The paper constructs a family answering all three negatively.
- Result
- Disproved
- Status
- Resolved
- AI contribution
- AI-assisted
- Method
- Construction
- Field
- Combinatorial Group Theory
- Posed by
- Gilbert Baumslag
- Year posed
- —
- Years open
- —
- Solved
- 2026-07-23
- Model
- ChatGPT
- Vendor
- OpenAI
- Collaborators
- Ke Wang, Qiang Zhang
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 20 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The paper's disclosure is a single sentence: ChatGPT assisted in constructing the examples. The examples are the result, but 'assisted' does not say how much, so the lowest tier applies.
Verification
No independent check, and the one-line disclosure does not separate the model's contribution from the authors'. Preprint, not refereed.