Computable torsion-free nilpotent groups of finite dimension. (Q404717)

One says that the dimension of a torsion-free nilpotent group \(G\) is finite if there exists a central series in \(G\) whose every section has finite dimension as Abelian group. A criterion for the computability (constructivizability) of a torsion-free nilpotent group of finite dimension is given. The existence of a principal computable enumeration of the class of all computable torsion-free nilpotent groups of finite dimension is proved. An example of a subgroup \(G\) in the group \(\text{UT}_3(\mathbb Q)\) of all unitriangular matrices of size \(3\times 3\) over the rationals is described, such that all the sections of any central series in \(G\) are computable, but \(G\) is not computable itself.