How Many Units Can a Commutative Ring Have?. Issue 10 (1st December 2017) - Chebolu, Sunil K.; Lockridge, Keir
Abstract: László Fuchs posed the following problem in 1960, which remains open: determine whether a given abelian group can occur as the group of units in a commutative ring. In this note, we provide an elementary solution to a simpler, related problem: find all cardinal numbers occurring as the cardinality of the group of units in a commutative ring. As a byproduct, we obtain a solution to Fuchs's problem for the class of finite abelian p -groups when p is an odd prime.