Conjugacy problem for residually nilpotent one‑relator groups

Ascertain whether the conjugacy problem is decidable for residually nilpotent one‑relator groups; i.e., determine if a general algorithm exists to decide conjugacy in any one‑relator group whose lower central series intersections are trivial.

Background

While finitely generated nilpotent groups are conjugacy separable and have decidable conjugacy problems, residually nilpotent groups can still have undecidable conjugacy problems. The authors note that the status for one‑relator groups that are residually nilpotent is unknown.

Resolving this would extend decidability frontiers within an important subclass of one‑relator groups.