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Let G be a definably compact group in an o-minimal expansion of a real closedfield. We prove that if dim(G X) < dim G for some definable X subset of G thenX contains a torsion point of G. Along the way we develop a general theory forso-called G-linear sets, and investigate definable sets which contain abstractsubgroups of G.

G-linear sets and torsion points in definably compact groups