Abstract
We study locally definable abelian groups \({\mathcal{U}}\) in various settings and examine conditions under which the quotient of \({\mathcal{U}}\) by a discrete subgroup might be definable. This turns out to be related to the existence of the type-definable subgroup \({\mathcal{U}^{00}}\) and to the divisibility of \({\mathcal{U}}\) .
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P. E. Eleftheriou 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 quotients of locally definable groups. Sel. Math. New Ser. 18, 885–903 (2012). https://doi.org/10.1007/s00029-012-0091-5
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DOI: https://doi.org/10.1007/s00029-012-0091-5