The order of the second group of units of the ring Z[i]/ < β >

Abstract

In this article we introduce a newely defined function $\phi _{G}^{2}(\beta )$ that represents the order of the second group of units of the ring $R=\mathbf{Z}[i]/<\beta >$. We examine some of the properties of this function that are similar to that of the Euler Phi function $\phi (n)$.