A Survey of Galois Theory
Date of Graduation
Master of Science in Mathematics
In this paper, we will see a summary of Galois theory and some results utilized in Algebra. We state and prove the Fundamental Theorem of Galois theory and then work a few examples to show its application to the determination of lattices of groups and fields. In Chapter 2, we prove the theorem which shows the connections between solvability of polynomials and groups and work a few examples demonstrating how to use groups to solve polynomials. In Chapter 3, we briefly consider the Inverse Problem of Galois theory where we consider arbitrary groups and try to find extensions for which they are the Galois group.
© Christina L Daniel
Daniel, Christina L., "A Survey of Galois Theory" (1995). MSU Graduate Theses. 866.