### A VISUAL MODEL FOR COMPUTING SOME PROPERTIES OF U(n) AND Zn

#### Abstract

A computer program is developed using Microsoft Visual C++ in theWindows environment. This program focuses on two specific finite Abelian groups, which are the group Zn under addition modulo n and the group U(n) under multiplication modulo n, where n is any positive integer less than or equal to 120. Computations of the properties of the two groups get more tedious and time consuming as the value of n increases. Therefore a program that could

assist in the computation would indeed be of great help. This program in C++ is written relating to some properties of Zn and U(n). It enables the user to enter any positive integer n (n · 120) to generate answers to some properties of these two groups. A lattice diagram can be obtained for any groups of Zn and, for groups of U(n) which are cyclic.

assist in the computation would indeed be of great help. This program in C++ is written relating to some properties of Zn and U(n). It enables the user to enter any positive integer n (n · 120) to generate answers to some properties of these two groups. A lattice diagram can be obtained for any groups of Zn and, for groups of U(n) which are cyclic.

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