ON GALOIS THEORY AND ITS APPLICATION TO SOLVABILITY OF POLYNOMIALS BY RADICALS

Abstract

It has been found that Galois Theory can be used to determine the solvability of polynomials over a field by radicals. This paper attempts to explore this theory with a view to apply it for the solvability of polynomials by radicals. Basic facts about basic algebraic structures such as normal groups quotient groups as well as solvable groups will be collected. Field extension especially normal extension and separable extension are of significant for our study. Galois group of a polynomials is defined and ways of determining it are given. Finally we shall focuses on the solvability of polynomials by radicals. Some general results in this direction are collected.