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Commutator Relators Do Not Force Hopficity, Residual Finiteness or Automaticity

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one-relator-groups-commutator-relatorsAlgebraposed by Gilbert Baumslagrecorded: disproved

1 attempt · no person has looked

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.

Context

Answers a question of Baumslag, a central figure in one-relator group theory, negatively on all three counts.

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  • #1

    Attempt 1

    constructionChatGPT with Ke Wang, Qiang Zhang ·
    AI involvement
    ai assisted
    — a person led the work and used a model along the way.
    models
    ChatGPT
    people
    Ke Wang, Qiang Zhang

    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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