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Splitting definably compact groups in o-minimal structures

Published online by Cambridge University Press:  12 March 2014

Marcello Mamino*
Affiliation:
Classe di Scienze - Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy, E-mail: [email protected]

Abstract

An argument of A. Borel [Bor-61, Proposition 3.1] shows that every compact connected Lie group is homeomorphic to the Cartesian product of its derived subgroup and a torus. We prove a parallel result for definably compact definably connected groups definable in an o-minimal expansion of a real closed field. As opposed to the Lie case, however, we provide an example showing that the derived subgroup may not have a definable semidirect complement.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2011

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References

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