Definable groups as homomorphic images of semi-linear and field-definable groups

Pantelis E. Eleftheriou; Ya'acov Peterzil

doi:10.1007/s00029-012-0092-4

Definable groups as homomorphic images of semi-linear and field-definable groups

Pantelis E. Eleftheriou
, Ya'acov Peterzil

Department of Mathematics

University of Haifa

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

Abstract

We analyze definably compact groups in o-minimal expansions of ordered groups as a combination of semi-linear groups and groups definable in o-minimal expansions of real closed fields. The analysis involves structure theorems about their locally definable covers. As a corollary, we prove the compact domination conjecture in o-minimal expansions of ordered groups.

Original language	American English
Pages (from-to)	905-940
Number of pages	36
Journal	Selecta Mathematica, New Series
Volume	18
Issue number	4
DOIs	https://doi.org/10.1007/s00029-012-0092-4
State	Published - Dec 2012

Keywords

Definable quotients
Locally definable groups
O-minimality
Semi-bounded structures
Type-definable groups

ASJC Scopus subject areas

General Mathematics
General Physics and Astronomy

Access to Document

10.1007/s00029-012-0092-4

Cite this

@article{49f806ce45f84be1877e773117e740f3,

title = "Definable groups as homomorphic images of semi-linear and field-definable groups",

abstract = "We analyze definably compact groups in o-minimal expansions of ordered groups as a combination of semi-linear groups and groups definable in o-minimal expansions of real closed fields. The analysis involves structure theorems about their locally definable covers. As a corollary, we prove the compact domination conjecture in o-minimal expansions of ordered groups.",

keywords = "Definable quotients, Locally definable groups, O-minimality, Semi-bounded structures, Type-definable groups",

author = "Eleftheriou, \{Pantelis E.\} and Ya'acov Peterzil",

note = "Funding Information: The first author was supported by the Funda{\c c}{\~a}o para a Ci{\^e}ncia e a Tecnologia grants SFRH/BPD/35000/2007 and PTDC/MAT/101740/2008.",

year = "2012",

month = dec,

doi = "10.1007/s00029-012-0092-4",

language = "American English",

volume = "18",

pages = "905--940",

journal = "Selecta Mathematica, New Series",

issn = "1022-1824",

number = "4",

}

TY - JOUR

T1 - Definable groups as homomorphic images of semi-linear and field-definable groups

AU - Eleftheriou, Pantelis E.

AU - Peterzil, Ya'acov

N1 - Funding Information: The first author was supported by the Fundação para a Ciência e a Tecnologia grants SFRH/BPD/35000/2007 and PTDC/MAT/101740/2008.

PY - 2012/12

Y1 - 2012/12

N2 - We analyze definably compact groups in o-minimal expansions of ordered groups as a combination of semi-linear groups and groups definable in o-minimal expansions of real closed fields. The analysis involves structure theorems about their locally definable covers. As a corollary, we prove the compact domination conjecture in o-minimal expansions of ordered groups.

AB - We analyze definably compact groups in o-minimal expansions of ordered groups as a combination of semi-linear groups and groups definable in o-minimal expansions of real closed fields. The analysis involves structure theorems about their locally definable covers. As a corollary, we prove the compact domination conjecture in o-minimal expansions of ordered groups.

KW - Definable quotients

KW - Locally definable groups

KW - O-minimality

KW - Semi-bounded structures

KW - Type-definable groups

UR - https://www.scopus.com/pages/publications/84870391259

U2 - 10.1007/s00029-012-0092-4

DO - 10.1007/s00029-012-0092-4

M3 - Article

SN - 1022-1824

VL - 18

SP - 905

EP - 940

JO - Selecta Mathematica, New Series

JF - Selecta Mathematica, New Series

IS - 4

ER -

Definable groups as homomorphic images of semi-linear and field-definable groups

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this