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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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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DOI: https://doi.org/10.1007/s00029-012-0092-4