Chennai Mathematical Institute


Colloquium Announcement
Date: June 9th 2022
Day: Thursday
Time: 3:30 - 4:30 pm
Venue: Seminar Hall (Hybrid Mode)
An overview of Fuchs’ problem

Sunil Chebolu
Illinois State University, USA.


More than 50 years ago, Fuchs asked which abelian groups can be the group of units of a commutative ring? Though progress has been made, the question remains open. I will present an overview of my joint work with Keir Lockridge on this problem. We answered this question for various classes of groups including indecomposable abelian groups, dihedral groups, quaternion groups and some p-groups. This work also gave us several new characterizations of Mersenne primes and Fermat primes.