Units of $\mathbb{Z}C_{p^n}$

Abstract

Let $p$ be a prime integer and $n,i$ be positive integers such that \linebreak $S=\{-1, \ θ, \ μ_i=1+θ+... + θ^{i-1} \ \mid 1 < i < \frac{p^n}{2}, \ gcd(p^n,i)=1 \}$ generates the group of units of $\mathbb{Z}[θ],$ where $θ$ is a primitive ${p^n}$--$th$ root of unity. Denote by $C_{p^n}$ the cyclic group of order $p^n.$ In this paper we describe explicitly a multiplicatively independent set which generates a complement to $\pm C_{p^n}$ in the group of units of the integral group ring of $C_{p^n}.$