Zhang's Question on Howson and Strongly Howson Groups
A group is Howson if the intersection of any two finitely generated subgroups is finitely generated, and strongly Howson if the rank of that intersection is bounded in terms of the two ranks. Zhang asked whether the two coincide for finitely generated groups. They do not.
- Result
- Disproved
- Status
- Resolved
- AI contribution
- AI co-developed
- Method
- Construction
- Field
- Group theory
- Posed by
- Zhang
- Year posed
- —
- Years open
- —
- Solved
- 2026-05-29
- Model
- ChatGPT
- Vendor
- OpenAI
- Collaborators
- Ke Wang, Qiang Zhang
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 10 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The disclosure credits ChatGPT with constructing the example in Section 2, which is the separating example the paper turns on, while stating the proofs are the authors'.
Verification
arXiv preprint; not yet peer-reviewed.
Source
arXiv:2605.30840 - Finitely generated Howson groups which are not strongly Howson