The problem of the classification of the nilpotent class 2 torsion free groups up to the geometrically equivalence

Details The problem of the classification of the nilpotent class 2 torsion free groups up to the geometrically equivalence The problem of the classification of the nilpotent class 2 torsion free groups up to the geometrically equivalence

2006-11-23

arxiv.org/abs/math/0611736v1

Mathematics

Group Theory

9 pages, continuation of http://arxiv.org/abs/math.GR/0411313

Scientific paper

In this paper we consider the problem of classification of the nilpotent class 2 finitely generated torsion free groups up to the geometric equivalence. By a very easy technique it is proved that this problem is equivalent to the problem of classification of the complete (in the Maltsev sense) nilpotent torsion free finite rank groups up to the isomorphism. This result, allows us to once more comprehend the complication of the problem of the classification of the quasi-varieties of nilpotent class 2 groups. It is well known that the variety of a nilpotent class s (for every s) groups is Noetherian. So the problem of the classification of the quasi-varieties generated even by a single nilpotent class 2 finitely generated torsion free group, is equivalent to the problem of classification of complete (in the Maltsev sense) nilpotent torsion free finite rank groups up to the isomorphism.

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