Computing Galois Groups over Q
Christian L. Wilson · DigitalCommons (California Polytechnic State University) · 2009
Galois theory is an area of modern algebra which provides a framework for transforming problems involving fields into more manageable problems involving groups. The fundamental theorem of Galois theory asserts that there exists a one-to-one correspondence between certain subfields of a splitting field of a polynomial and the subgroups of its Galois group. This realization provides an elegant answer to the question of whether a polynomial equation over a base field is solvable by radicals. In fact, a polynomial is solvable by radicals if its Galois group is a solvable group. In general, the determination of the Galois group of a polynomial is not itself a trivial task, thus the determination of Galois groups provides a basis for the content of this thesis. More specifically, this thesis is concerned with the determination of Galois groups using resolvent polynomials from theory to implementation.