Groups of Units of Finite Commutative Group Rings*

Abstract

Let R be a finite commutative ring with identity and ℤ p d be the cyclic group of prime power order. Define Rℤ p d to mean the group ring of ℤ p d over R. We determine the structure of the group of units of Rℤ p d in the case when R is generated by an element whose order is not divisible by p.