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Commutator Relators Do Not Force Hopficity, Residual Finiteness or Automaticity

Algebra · posed by Gilbert Baumslag · disproved

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Statement

Baumslag asked whether a one-relator group G=F/⟨⟨r⟩⟩G=F/\langle\langle r\rangle\rangle with rr a commutator is Hopfian, residually finite or automatic. The paper constructs a family Gm=⟨a,t∣[t,a[a,t]−m]⟩G_m=\langle a,t \mid [t,a[a,t]^{-m}]\rangle answering all three negatively.

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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 assisted
    — a person led the work and used a model along the way.

    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.

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

open in Claude →open in ChatGPT →

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