### 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 $\phi (n)$.

**How to Cite this Article:**Wiam M. Zeid, The order of the second group of units of the ring Z[i]/ < β >, Journal of Mathematical and Computational Science, Vol 7, No 1 (2017), 30-38 Copyright © 2017 Wiam M. Zeid. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Journal of Mathematical and Computational Science

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