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

All Science Journal Classification (ASJC) codes

General Physics and Astronomy
General Mathematics

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10.1007/s00029-012-0092-4

Cite this

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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.",

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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

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ER -

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

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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