G-linear sets and torsion points in definably compact groups

Margarita Otero; Ya'Acov Peterzil

doi:10.1007/s00153-009-0128-4

G-linear sets and torsion points in definably compact groups

Margarita Otero, Ya'Acov Peterzil

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let G be a definably compact group in an o-minimal expansion of a real closed field. We prove that if dim(G\X) < dim G for some definable ⊆ G then X contains a torsion point of G. Along the way we develop a general theory for the so-called G-linear sets, and investigate definable sets which contain abstract subgroups of G.

Original language	English
Pages (from-to)	387-402
Number of pages	16
Journal	Archive for Mathematical Logic
Volume	48
Issue number	5
DOIs	https://doi.org/10.1007/s00153-009-0128-4
State	Published - Jun 2009

Bibliographical note

Funding Information:
M. Otero was Partially supported by GEOR MTM2005-02568 and Grupos UCM 910444.

Keywords

Definable group
O-Minimality
Torsion point

ASJC Scopus subject areas

Philosophy
Logic

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10.1007/s00153-009-0128-4

Cite this

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abstract = "Let G be a definably compact group in an o-minimal expansion of a real closed field. We prove that if dim(G\X) < dim G for some definable ⊆ G then X contains a torsion point of G. Along the way we develop a general theory for the so-called G-linear sets, and investigate definable sets which contain abstract subgroups of G.",

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N2 - Let G be a definably compact group in an o-minimal expansion of a real closed field. We prove that if dim(G\X) < dim G for some definable ⊆ G then X contains a torsion point of G. Along the way we develop a general theory for the so-called G-linear sets, and investigate definable sets which contain abstract subgroups of G.

AB - Let G be a definably compact group in an o-minimal expansion of a real closed field. We prove that if dim(G\X) < dim G for some definable ⊆ G then X contains a torsion point of G. Along the way we develop a general theory for the so-called G-linear sets, and investigate definable sets which contain abstract subgroups of G.

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KW - O-Minimality

KW - Torsion point

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ER -

G-linear sets and torsion points in definably compact groups

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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