ALGORITHMIC PROBLEMS IN TENSOR COMPLETIONS OF 2-NILPOTENT FINITELY GENERATED TORSION-FREE GROUPS

In this paper, we study algorithmic problems in tensor completions G⊗_N2,R R of finitely generated torsion-free nilpotent groups G of class 2 in the quasivariety N_2,R of R-exponential 2-nilpotent groups over a computable field of characteristic zero with a computable additive basis. We show that the word problem, the conjugacy problem, and the power problem are decidable in G ⊗_N2,R R. Note that these results do not hold for arbitrary finitely generated torsion-free 2-nilpotent R-groups. In fact, there are two generated torsion-free 2-nilpotent R-groups for which these problems are undecidable.