Computable torsion-free nilpotent groups of finite dimension

2014

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DOI 10.1134/s0037446614030094
Data confidence 70 medium
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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.