An Algorithm for the Free Generators of a Free Subgroup.

Group Theory has diverse applications in mathematics and has been used to solve real-world problems, such as in cryptography, computer graphics, molecular systems biology, and crystal studies. In this article, we delve into a detailed analysis of subgroups of the free group of rank 2. The primary focus of this study is to develop an intuitive visualization for constructing a free set of generators for a free subgroup, using a graph-theoretic approach based on Stallings Foldings to provide a topological interpretation and solution to the problem. This algorithm leverages the connection between algebraic structures and geometric constructs, allowing for an intuitive understanding of the structure of a free group. An implementation of this algorithm is included in Python, making it immediately useful for computational applications. [ABSTRACT FROM AUTHOR]