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On the Euler characteristic of definable groups
Mathematical Logic Quarterly 57 (1):44-46 (2011)
Abstract
We show that in an arbitrary o-minimal structure the following are equivalent: conjugates of a definable subgroup of a definably connected, definably compact definable group cover the group if the o-minimal Euler characteristic of the quotient is non zero; every infinite, definably connected, definably compact definable group has a non trivial torsion pointLinks
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References found in this work
Definably compact Abelian groups.Mário J. Edmundo & Margarita Otero - 2004 - Journal of Mathematical Logic 4 (02):163-180.
Definable homomorphisms of abelian groups in o-minimal structures.Ya'acov Peterzil & Sergei Starchenko - 1999 - Annals of Pure and Applied Logic 101 (1):1-27.
Combinatorics with definable sets: Euler characteristics and grothendieck rings.Jan Krajíček & Thomas Scanlon - 2000 - Bulletin of Symbolic Logic 6 (3):311-330.
Combinatorics with definable sets: Euler characteristics and Grothendieck rings.Jan Krají Cek & Thomas Scanlon - 2000 - Bulletin of Symbolic Logic 6 (3):311-330.
Groups Definable in Ordered Vector Spaces over Ordered Division Rings.Pantelis E. Eleftheriou & Sergei Starchenko - 2007 - Journal of Symbolic Logic 72 (4):1108 - 1140.
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