# Precompact noncompact reflexive Abelian groups

@inproceedings{ArdanzaTrevijano2010PrecompactNR, title={Precompact noncompact reflexive Abelian groups}, author={Sergio Ardanza-Trevijano and Mar{\'i}a Jes{\'u}s Chasco and Xabier Dom{\'i}nguez and Mikhail Tkachenko}, year={2010} }

Abstract. We study Pontryagin reflexivity in the class of precompact topological Abelian groups. We find reflexive groups among precompact not pseudocompact and among pseudocompact not compact groups. Making use of Martin's axiom we give an example of a reflexive countably compact not compact Abelian group. We also prove that every pseudocompact Abelian group is a quotient of a reflexive pseudocompact group with respect to a closed reflexive pseudocompact subgroup.

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