Journal of Symbolic Logic
- J. Symbolic Logic
- Volume 76, Issue 3 (2011), 973-986.
Splitting definably compact groups in o-minimal structures
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.
J. Symbolic Logic, Volume 76, Issue 3 (2011), 973-986.
First available in Project Euclid: 6 July 2011
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Mamino, Marcello. Splitting definably compact groups in o-minimal structures. J. Symbolic Logic 76 (2011), no. 3, 973--986. doi:10.2178/jsl/1309952529. https://projecteuclid.org/euclid.jsl/1309952529