Elementary coordinatization of finitely generated nilpotent groups

17 May 2016  ·  Myasnikov A. G., Sohrabi Mahmood ·

This paper has two main parts. In the first part we develop an elementary coordinatization for any nilpotent group $G$ taking exponents in a binomial principal ideal domain (PID) $A$... In case that the additive group $A^+$ of $A$ is finitely generated we prove using a classical result of Julia Robinson that one can obtain a central series for $G$ where the action of the ring of integers $\Z$ on the quotients of each of the consecutive terms of the series except for one very specific gap, called the special gap, is interpretable in $G$. Then we use a refinement of this central series to give a criterion for elementary equivalence of finitely generated nilpotent groups in terms of the relationship between group extensions and the second cohomology group. read more

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Group Theory Logic