Abstract:
We find criteria for the computability (constructivizability) of torsion-free nilpotent groups of finite dimension. We prove the existence of a principal computable enumeration of the class of all computable torsion-free nilpotent groups of finite dimension. An example is constructed of a subgroup in the group of all unitriangular matrices of dimension 3 over the field of rationals that is not computable but the sections of any of its central series are computable.
Keywords:dimension of a group, nilpotent torsion-free group of finite dimension, unitriangular matrix over the fields of rationals, central series, sections of the central series, computable group, principal computable enumeration.