Submission date: 6n November 2013.

Abstract:

This paper has two main parts. In the first part we develop an elementary coordinatization for any nilpotent group taking exponents in a binomial PID A. In case that the additive group A^+ of the A is finitely generated we prove using a classical result of Julia Robinson that one can obtain an elementary Z-coordinatization of the group. In the second part we use a refinement of the Z-coordinatization obtained above to give a new structural and algebraic criterion for elementary equivalence of finitely generated nilpotent groups.

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Full text arXiv 1311.1391: pdf, ps.