This award supports research on the structure of certain classes of finite rank indecomposable Butler groups, co-purely-indecomposable modules over a discrete valuation ring, and finitely generated indecomposable modules over pullback rings. Included are projects for classification by invariants. Particular attention will be devoed to determining finite, tame, or wild representation type for each class considered. Infinite dimensional Z-representations will be used to investigate problems revolving around realizations of (nonabelian) groups as automorphism groups of fields. This project is in the general area of abelian group theory. It is concerned with the classification of abelian groups and the application of this knowledge to other areas. 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.
