Submission date: 3 August 2007

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 subset X of G then X contains a torsion point of G. Along the way we develop a general theory for so-called G-linear sets, and investigate definable sets which contain abstract subgroups of G. 

Mathematics Subject Classification: 03C64

Keywords and phrases: o-minimality, definable group, torsion point

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