Abstract

The Inverse Galois Problem, initially formulated by Évariste Galois in the 19th century, aims to understand the structural characteristics and representation of specific groups as Galois groups over fields. This research paper provides a comprehensive analysis of the structural properties and representation of groups that arise within the context of the Inverse Galois Problem. By examining various approaches and techniques, we aim to elucidate the complexity and underlying patterns within these groups.Keywords: Inverse Galois Problem, Galois groups, structural characteristics, representation, group theory, group classification, Galois cohomology, computational methods.