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September 2011 Splitting definably compact groups in o-minimal structures
Marcello Mamino
J. Symbolic Logic 76(3): 973-986 (September 2011). DOI: 10.2178/jsl/1309952529

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.

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Marcello Mamino. "Splitting definably compact groups in o-minimal structures." J. Symbolic Logic 76 (3) 973 - 986, September 2011. https://doi.org/10.2178/jsl/1309952529

Information

Published: September 2011
First available in Project Euclid: 6 July 2011

zbMATH: 1247.03062
MathSciNet: MR2849254
Digital Object Identifier: 10.2178/jsl/1309952529

Subjects:
Primary: 03C64, 55S40

Rights: Copyright © 2011 Association for Symbolic Logic

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Vol.76 • No. 3 • September 2011
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