A descending chain condition for groups definable in o -minimal structures

Annals of Pure and Applied Logic 134 (2):303-313 (2005)

Abstract
We prove that if G is a group definable in a saturated o-minimal structure, then G has no infinite descending chain of type-definable subgroups of bounded index. Equivalently, G has a smallest type-definable subgroup G00 of bounded index and G/G00 equipped with the “logic topology” is a compact Lie group. These results give partial answers to some conjectures of the fourth author
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DOI 10.1016/j.apal.2005.01.002
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References found in this work BETA

Type-Definability, Compact Lie Groups, and o-Minimality.Anand Pillay - 2004 - Journal of Mathematical Logic 4 (02):147-162.
Definably Compact Abelian Groups.Mário J. Edmundo & Margarita Otero - 2004 - Journal of Mathematical Logic 4 (02):163-180.
Intersection Theory for o-Minimal Manifolds.Alessandro Berarducci & Margarita Otero - 2001 - Annals of Pure and Applied Logic 107 (1-3):87-119.
One-Dimensional Groups Over an o-Minimal Structure.Vladimir Razenj - 1991 - Annals of Pure and Applied Logic 53 (3):269-277.
Transfer Methods for o-Minimal Topology.Alessandro Berarducci & Margarita Otero - 2003 - Journal of Symbolic Logic 68 (3):785-794.

View all 6 references / Add more references

Citations of this work BETA

O-Minimal Spectra, Infinitesimal Subgroups and Cohomology.Alessandro Berarducci - 2007 - Journal of Symbolic Logic 72 (4):1177 - 1193.
One-Basedness and Groups of the Form G/G 00.Davide Penazzi - 2011 - Archive for Mathematical Logic 50 (7-8):743-758.

View all 8 citations / Add more citations

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