The computation of some properties of additive and multiplicative groups of integers modulo n using C++ programming

Abstract

This research is focused on two types of finite abelian groups which are the group of integers under addition modulo , and the group of integers under multiplication modulo , where is any positive integer at most 200. The computations of some properties of the group including the order of the group, the order and inverse of each element, the cyclic subgroups, the generators of the group, and the lattice diagrams get more complicated and time consuming as n increases. Therefore, a special program is needed in the computation of these properties. Thus in this research, a program has been developed by using Microsoft Visual C++ Programming. This program enables the user to enter any positive integer at most 200 to generate answers for the properties of the groups.