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Equational Noethericity of Metabelian r-Groups

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Abstract

The author had earlier defined the concept of an r-group, generalizing the concept of a rigid (solvable) group. This article proves that every metabelian r-group is equationally Noetherian; i.e., each system of equations in finitely many variables with coefficients in the group is equivalent to some finite subsystem.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk State University, Novosibirsk, Russia

    N. S. Romanovskii

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  1. N. S. Romanovskii
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Correspondence to N. S. Romanovskii.

Additional information

Russian Text © The Author(s), 2020, published in Sibirskii Matematicheskii Zhurnal, 2020, Vol. 61, No. 1, pp. 194–200.

The author was supported by the Russian Foundation for Basic Research (Grant 18-01-00100).

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Romanovskii, N.S. Equational Noethericity of Metabelian r-Groups. Sib Math J 61, 154–158 (2020). https://doi.org/10.1134/S0037446620010139

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  • DOI: https://doi.org/10.1134/S0037446620010139

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