Commutator Relators Do Not Force Hopficity, Residual Finiteness or Automaticity
Baumslag asked whether a one-relator group $G=F/\langle\langle r\rangle\rangle$ with $r$ a commutator is Hopfian, residually finite or automatic. The paper constructs a family $G_m=\langle a,t \mid [t,a[a,t]^{-m}]\rangle$ answering all three negatively.
Exact FrontierDelta
Scope and record
Occurred: Jul 23, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-assisted. Imported under CC BY 4.0.
Canonical aliases: Commutator Relators Do Not Force Hopficity, Residual Finiteness or Automaticity · One-relator groups
Confidence: Not scored
Registry verification: unreviewed · preprint · resolved
Attribution
VibeMathed
registry · event recorded by
Ke Wang
human · human collaborator
Qiang Zhang
human · human collaborator
ChatGPT
model · ai model contributor · OpenAI
Lineage and corrections
This event attributed to Qiang Zhang
This event attributed to Ke Wang
This event attributed to ChatGPT