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

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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.

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Authors and Affiliations

  1. CMAF, Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649-003, Lisboa, Portugal

    Pantelis E. Eleftheriou

  2. Department of Mathematics, University of Haifa, Haifa, Israel

    Ya’acov Peterzil

Authors
  1. Pantelis E. Eleftheriou
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  2. Ya’acov Peterzil
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Correspondence to Ya’acov Peterzil.

Additional 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.

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Eleftheriou, P.E., Peterzil, Y. Definable groups as homomorphic images of semi-linear and field-definable groups. Sel. Math. New Ser. 18, 905–940 (2012). https://doi.org/10.1007/s00029-012-0092-4

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