A study on constructive inverse Galois problem

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Galois theory, forms the foundation of modern algebra, founded by Evariste Galois has continued to support the development of state-of-the-art mathematics. In Galois theory, the problem "whether every finite group appears as the Galois group of some field extension or not" is called inverse Galois problem, and is related to the structure of the absolute Galois group of rationals which is an interesting subject in number theory.In this research, we gave answers to some problems, e.g. Noether's problem, the field isomorphism problem of generic polynomials, which are related to the inverse Galois problem. By applying this, we also solved some Thue equations.