Product of two groups integers modulo m,n and their factor groups using python

Abstract

Abstract We all know that (Z m ×Z n ,+) is a group under addition modulo m and n. Recall that a cyclic subgroup is a subgroup that generated by one element in the group. We can get the group factor of all cyclic subgroups in a group (Z m ×Z n ,+) since any their cyclic subgroup is normal On the other hand, Python is a programming language that is multipurpose, easy to use, and also can run on various OS like Windows, Ubuntu, or Android. Moreover, the modulo operations on groups (Z m × Z n ,+) also can be calculated by Python, so we can use Python to get the factor groups off all their cyclic subgroups. In this paper, we determine the group factor in a group (Z m ×Z n ,+) of any cyclic subgroup using Python.