Central Units in ℤCp, q

Abstract

Let Cp, q be the semi-direct product of a cyclic group of order q by a cyclic group of order p, and ℤCp, q the integral group ring of Cp, q. In this article, firstly, we describe the group of normalized central units of ℤCp, q as a direct product of two subgroups that we call units of first kind and of second kind. For a class of prime numbers that we call good primes, we construct a multiplicatively independent set which generates the group of units of first kind. Finally, we construct a set of multiplicatively independent units which generates the units of second kind for a larger class of primes.