Groups, Geometry, and Dynamics

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Volume 1, Issue 1, 2007, pp. 1–20
DOI: 10.4171/GGD/1

Published online: 2007-03-31

The isomorphism problem for residually torsion-free nilpotent groups

Gilbert Baumslag and Charles F. Miller III[1]

(1) University of Melbourne, Melbourne, Australia

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.

Keywords: Finitely presented group, isomorphism problem, residually nilpotent

Baumslag Gilbert, Miller III Charles: The isomorphism problem for residually torsion-free nilpotent groups. Groups Geom. Dyn. 1 (2007), 1-20. doi: 10.4171/GGD/1