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

Pantelis E. Eleftheriou, Ya'acov Peterzil

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)905-940
Number of pages36
JournalSelecta Mathematica, New Series
Volume18
Issue number4
DOIs
StatePublished - Dec 2012

Bibliographical note

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.

Keywords

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

ASJC Scopus subject areas

  • Mathematics (all)
  • Physics and Astronomy (all)

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