Real Algebraic and Analytic Geometry |

G-linear sets and torsion points in definably compact groups.

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Submission: 2007, August 3.

*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 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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