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

Access to Document

10.1007/s00153-009-0128-4

Cite this

@article{1722c632d33b409ca9ee2de77334da26,

title = "G-linear sets and torsion points in definably compact groups",

abstract = "Let G be a definably compact group in an o-minimal expansion of a real closed field. We prove that if dim(G\textbackslash{}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.",

keywords = "Definable group, O-Minimality, Torsion point",

author = "Margarita Otero and Ya'Acov Peterzil",

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

year = "2009",

month = jun,

doi = "10.1007/s00153-009-0128-4",

language = "English",

volume = "48",

pages = "387--402",

journal = "Archive for Mathematical Logic",

issn = "0933-5846",

publisher = "Springer New York",

number = "5",

}

TY - JOUR

T1 - G-linear sets and torsion points in definably compact groups

AU - Otero, Margarita

AU - Peterzil, Ya'Acov

N1 - Funding Information: M. Otero was Partially supported by GEOR MTM2005-02568 and Grupos UCM 910444.

PY - 2009/6

Y1 - 2009/6

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.

KW - Definable group

KW - O-Minimality

KW - Torsion point

UR - https://www.scopus.com/pages/publications/67349203390

U2 - 10.1007/s00153-009-0128-4

DO - 10.1007/s00153-009-0128-4

M3 - Article

AN - SCOPUS:67349203390

SN - 0933-5846

VL - 48

SP - 387

EP - 402

JO - Archive for Mathematical Logic

JF - Archive for Mathematical Logic

IS - 5

ER -

G-linear sets and torsion points in definably compact groups

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this