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 ⊆ 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.
|Number of pages||16|
|Journal||Archive for Mathematical Logic|
|State||Published - Jun 2009|
Bibliographical noteFunding Information:
M. Otero was Partially supported by GEOR MTM2005-02568 and Grupos UCM 910444.
- Definable group
- Torsion point
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