A graph-based approach for the solution of some congruence equations

In this thesis, three cases that make Nor(N) is a triangular group were examined separately. For this, in each case concerned that vertex sets where transitive action is provided were determined, the conditions for the two corners to be in the same block by determining the subgroup that makes imprimitive movement is possible, were determined, double transitive properties which means that edge condition were founded, what types of circuits are in the subgraph using the edge condition are investigated. The present study consists of two main chapters. In the first part, we try to summarize some general knowledge which are related our problem from algebra and number theory. At the end of the section we show an example which uses a bridge between algebra and analysis. In the second part we expressed our method and calculations via suborbital graphs. Key Words: Modular group, Suborbital graphs, Normalizer