Action of G and Q(√ m) and algorithmic implementation for group actions

This paper calls for a relationship among the actions of groups G and M on Q(√m). It characterized several significant elements of G in terms of generators of M and vice versa. In this way we cultivate a correlation between the rudiments of these two modular groups. This will help us in discovering various G and M-Subsets of Q(√m). We have also generated an algorithm by using Visual Basic for calculating the congruence classes of different Moduli and manipulating the group actions.

Keywords:

Mobius Groups , Quadratic Fields , Generators , Group Action