Applications of Group Actions in Algebraic Structures

In abstract algebra and other branches of mathematics, the concept of a large group of individuals collaborating on a gives a strong foundation for comprehending how a group can symmetrically transform the elements of a set. The thesis centers on exploring and resolving the complexities associated with group actions on sets, particularly in terms of their advanced theoretical aspects and practical applications. This research seeks to push the boundaries of current knowledge, providing new insights and tools for both theoretical and applied mathematics. Using software tools like Mathematica, MATLAB, or GAP (Groups, Algorithms, and Programming) to simulate group actions and visualize their effects on sets and to implement algorithms for solving group action-related problems, such as computing orbits, stabilizers, and automorphism groups. This study helps in analyzing the efficiency and scalability of these algorithms, particularly in handling large or complex groups.