Groups of Units of Finite Commutative Group Rings*

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