Submission date: 4 August 2010.

Abstract:

We show that in an o-minimal expansion of an ordered group finite definable extensions of a definable group which is defined in a reduct are already defined in the reduct. A similar result is proved for finite topological extensions of definable groups defined in o-minimal expansions of the ordered set of real numbers.

Mathematics Subject Classification: 03C64, 20E99

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

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