Old and recent results on reflexive abelian groups
by
Rüdiger Göbel
Universität Essen

The oldest non-trivial examples in abelian group theory of reflexive groups (those where the evaluation map is an isomorphism) are related with a well known theorem of J. Los. Later quite sophisticated reflexive groups and more generally dual groups (those isomorphic to Hom(G, Z) for some group G) are connected with Eda-Otah's theory of continuous functions, for details see the book by Eklof Mekler. I will discuss some of these constructions. An open problem (No. 12 in the book by Eklof Mekler) will be answered (= very recent joint work with Saharon Shelah): There are reflexive groups G such that G is not isomorphic to G \oplusZ. (we require ZFC + CH). The proof is based on a nice theory of bilinear forms and a Hahn-Banach type theorem on free abelian groups.

Date received: July 29, 1999