G-linear sets and torsion points in definably compact groups

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Archive for Mathematical Logic 48 (5):387-402 (2009)
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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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10.1007/s00153-009-0128-4

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Citations of this work

Locally definable homotopy.Elías Baro & Margarita Otero - 2010 - Annals of Pure and Applied Logic 161 (4):488-503.
Locally definable homotopy.Elías Baro & Marg\ Otero - 2010 - Annals of Pure and Applied Logic 161 (4):488-503.

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References found in this work

Definably compact Abelian groups.Mário J. Edmundo & Margarita Otero - 2004 - Journal of Mathematical Logic 4 (02):163-180.
[Omnibus Review].Ehud Hrushovski - 1993 - Journal of Symbolic Logic 58 (2):710-713.
A remark on divisibility of definable groups.Mário J. Edmundo - 2005 - Mathematical Logic Quarterly 51 (6):639-641.
Transfer methods for o-minimal topology.Alessandro Berarducci & Margarita Otero - 2003 - Journal of Symbolic Logic 68 (3):785-794.

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