9405118 Keef This award supports research on p-local abelian groups, that is modules over the integers localized at the prime p. The principal investigator will apply some of the new approaches of abelian group theory to the theory of p-alpha-purity. Of particular importance are tools stemming from the increasing interplay between set-theory and abelian groups, recent work on the structure of the torsion product, important structure theorems relating to the class of IT groups, the theory of valuated groups and vector spaces, and the higher derived functors of the inverse limit. This project is in the general area of abelian group theory and is concerned with the classification of abelian groups. Although the classification of finite abelian groups has been well understood for a century, the classification of infinite abelian groups remains elusive. This research involves this old problem of classification of the infinite abelian groups approached by new tools from logic and topology.
