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Two remarks on the first-order theories of Baumslag-Solitar groups

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Abstract

We characterize all finitely generated groups elementarily equivalent to a solvable Baumslag-Solitar group BS(m, 1). It turns out that a finitely generated group G is elementarily equivalent to BS(m, 1) if and only if G is isomorphic to BS(m, 1). Furthermore, we show that two Baumslag-Solitar groups are existentially (universally) equivalent if and only if they are elementarily equivalent if and only if they are isomorphic.

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Authors and Affiliations

  1. Stevenson Center and Vanderbilt University, Nashville, USA

    M. Casals-Ruiz & I. V. Kazachkov

Authors
  1. M. Casals-Ruiz
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  2. I. V. Kazachkov
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Correspondence to M. Casals-Ruiz.

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Original Russian Text Copyright © 2012 Casals-Ruiz M. and Kazachkov I.V.

The work done during a visit to the Omsk Department of the Sobolev Institute of Mathematics of the Siberian Division of the Russian Academy of Sciences. The authors thank the staff of the Institute and especially V. N. Remeslennikov for hospitality. The first author was supported by Programa de Formación de Investigadores del Departamento de Educación, Universidades e Investigación del Gobierno Vasco. The second author was supported by the NSERC Postdoctoral Fellowship.

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Nashville. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 53, No. 5, pp. 1007–1012, September–October, 2012.

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Casals-Ruiz, M., Kazachkov, I.V. Two remarks on the first-order theories of Baumslag-Solitar groups. Sib Math J 53, 805–809 (2012). https://doi.org/10.1134/S0037446612050060

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  • DOI: https://doi.org/10.1134/S0037446612050060

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