Real Algebraic and Analytic Geometry
Submission: 2007, August 3.
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 subset 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 (2000): 03C64.
Keywords and Phrases: o-minimality, definable group, torsion point.
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