Central Units in ℤC_{p, q}

Abstract

Let C_{p, q} be the semi-direct product of a cyclic group of order q by a cyclic group of order p, and ℤC_{p, q} the integral group ring of C_{p, q}. In this article, firstly, we describe the group of normalized central units of ℤC_{p, 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.

Key Words:

• Central units
• Finite groups
• Group rings
• Metacyclic groups

2010 Mathematics Subject Classification:

• Primary: 16S34
• Secondary: 20C10