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Residual finiteness of hyperbolic one-relator groups

Establish whether all hyperbolic one-relator groups are residually finite.

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Background

Residual finiteness is known for many hyperbolic groups but is not guaranteed universally. For one-relator groups, residual finiteness enables strong profinite and algorithmic properties; its status for hyperbolic cases is currently unknown.

References

It is not known whether hyperbolic one-relator groups are residually finite.

— The theory of one-relator groups: history and recent progress (2501.18306 - Linton et al., 30 Jan 2025) in Subsection 6.1 (Hyperbolic one-relator groups)