Mathematical Sciences: Invariants for Abelian Groups and Representations of Posets

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The primary goal of this research is the study of the invariants for a class of torsion-free Abelian groups of finite rank known as the Butler groups. The invariants are to be examined concurrently in the context of representations of finite partially ordered sets. A study of Coxeter correspondences and almost split sequences is included in the project with the aim of expanding the menu of potentially classifiable groups and representations. The research is in the general area of algebra and is concerned with the structure theory of infinite groups having a commutative multiplicative structure - the Abelian groups. These groups arise in a variety of settings in algebra, geometry, and analysis. This research concerns the classification of invariants for selected families of these Abelian groups in anticipation of obtaining a general structure theory.