Mathematical Sciences: Endomorphisms of Groups and Modules

本课题主要研究群和模的自同态。主要的调查者将研究某些Butler群的自同态环，并根据它们的自然滤子对它们进行分类。此外，还将研究作为模的自由阿贝尔群的自同态环、二类幂零群的自同构群和局部有限群的自同构群。本研究属于交换群论的一般领域。交换群是定义了交换乘法的代数结构。这一领域目前正在影响着数学的几个领域，包括集合论、环论和群论。

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.