#### IMSc Webinar

#### How many units can a commutative ring have?

#### Sunil Chebolu

##### Illinois State University

*Laszlo Fuchs posed the following problem in 1960, which remains open: classify the abelian groups occurring as the group of all units in a commutative ring. In this talk, I will provide an elementary solution to a simpler, related problem: find all cardinal numbers occurring as the cardinality of the group of all units in a commutative ring. As a by-product, we obtain a solution to Fuchs' problem for the class of finite abelian p-groups when p is an odd prime.*

zoom.us/j/91288928049?pwd=WHNaUE9TZEdZWGR3aGNtN2JvWDNtZz09

Done