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G-linear sets and torsion points in definably compact groups

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Abstract

Let G be a definably compact group in an o-minimal expansion of a real closed field. We prove that if dim(G\X) < dim G for some definable \({X \subseteq G}\) then X contains a torsion point of G. Along the way we develop a general theory for the so-called G-linear sets, and investigate definable sets which contain abstract subgroups of G.

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049, Madrid, Spain

    Margarita Otero

  2. Department of Mathematics, University of Haifa, Haifa, Israel

    Ya’acov Peterzil

Authors
  1. Margarita Otero
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  2. Ya’acov Peterzil
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Corresponding author

Correspondence to Margarita Otero.

Additional information

M. Otero was Partially supported by GEOR MTM2005-02568 and Grupos UCM 910444.

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Otero, M., Peterzil, Y. G-linear sets and torsion points in definably compact groups. Arch. Math. Logic 48, 387–402 (2009). https://doi.org/10.1007/s00153-009-0128-4

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  • DOI: https://doi.org/10.1007/s00153-009-0128-4

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