Mathematical Sciences: A Relative Structure Theory for Abelian Groups

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This project is concerned with developing a theory of relative structure for abelian groups. The approach is through a series of equivalence theorems. The principal investigator will concentrate on Butler groups and global Warfield groups. In particular, the research will focus on establishing an equivalence theorem for arbitrary pure subgroups of completely decomposable groups. 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 analysis.