English

Inverse Galois Problem and Significant Methods

History and Overview 2015-12-31 v1 Algebraic Geometry

Abstract

The inverse problem of Galois Theory was developed in the early 1800 s as an approach to understand polynomials and their roots. The inverse Galois problem states whether any finite group can be realized as a Galois group over Q (field of rational numbers). There has been considerable progress in this as yet unsolved problem. Here, we shall discuss some of the most significant results on this problem. This paper also presents a nice variety of significant methods in connection with the problem such as the Hilbert irreducibility theorem, Noether s problem, and rigidity method and so on.

Keywords

Cite

@article{arxiv.1512.08708,
  title  = {Inverse Galois Problem and Significant Methods},
  author = {Fariba Ranjbar and Saeed Ranjbar},
  journal= {arXiv preprint arXiv:1512.08708},
  year   = {2015}
}

Comments

11 pages, 2 figures. arXiv admin note: text overlap with arXiv:1112.1522 by other authors without attribution

R2 v1 2026-06-22T12:19:32.679Z