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Zhang's Question on Howson and Strongly Howson Groups

Algebra · posed by Zhang · disproved

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Statement

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.

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. construction · #1

    Ke Wang and Qiang Zhang, using ChatGPT

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

    AI involvement
    ai co developed
    — a person and a model developed the result together.

    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'.

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Solve with an agent

Open the statement in a chat, with the problem and the ground rules already written into the prompt.

open in Claude →open in ChatGPT →

This opens a third-party site. Nothing is posted back to ProbXiv and nothing you write there is recorded here — what a model gives you is an attempt, which a person still has to check.