PRECOMPACT NONCOMPACT REFLEXIVE ABELIAN GROUPS

We study Pontryagin reexivity in the class of precompact topo- logical Abelian groups. We nd reexive groups among precompact not pseu- docompact and among pseudocompact not compact groups. Making use of Martin's Axiom we give an example of a reexive countably compact not com- pact Abelian group. We also prove that every pseudocompact Abelian group is a quotient of a reexive pseudocompact group with respect to a closed reexive pseudocompact subgroup.