Mathematical Sciences: Endomorphisms of Groups and Modules

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This project is concerned with the endomorphisms of groups and modules. The pricipal investigator will examine the endomorphism rings of certain Butler groups and will classify them in terms of their natural filtrations. Research will also be done on torsion-free abelian groups as modules over their rings of endomorphisms, automorphism groups of nilpotent groups of class two and automorphism groups of locally finite groups. This research is in the general area of abelian group theory. An abelian group is an algebraic structure with a commutative multiplication defined on it. This area is currently impacting several areas of mathematics including set theory, ring theory and group theory.