Sunil Chebolu (Illinois State University): An Overview of Fuchs' Problem

Over 50 years ago, László Fuchs posed a fundamental question in algebra: Which abelian groups can arise as the group of units of a commutative ring? Despite significant progress, this question remains largely open. In this talk, I will provide an overview of my joint work with Keir Lockridge on this problem and its variations. We have resolved Fuchs' question for several classes of groups, including indecomposable abelian groups, dihedral groups, quaternion groups, and certain p-groups. Additionally, our work led to new characterizations of Mersenne and Fermat primes.