Submission date: 4 August 2010.

Abstract:

We show that in an arbitrary o-minimal structure the following are equivalent: (i) conjugates of a definable subgroup of a definably connected, definably compact definable group cover the group if the o-minimal Euler characteristic of the quotient is non zero; (ii) every infinite, definably connected, definably compact definable group has a non trivial torsion point.

Mathematics Subject Classification: 03C64, 55N30.

Keywords and phrases: O-minimal structures, definable groups.

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