Both the conjugacy and isomorphism problems for finitely generated nilpotent groups are recursively solvable. In some recent work, the first author, with a tiny modification of work in the second author's thesis, proved that the conjugacy problem for finitely presented, residually torsion-free nilpotent groups is recursively unsolvable. Here we complete the algorithmic picture by proving that the isomorphism problem for such groups is also recursively unsolvable.
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Gilbert Baumslag, Charles F. Miller III, The isomorphism problem for residually torsion-free nilpotent groups. Groups Geom. Dyn. 1 (2007), no. 1, pp. 1–20DOI 10.4171/GGD/1