Date of Defense
John Petro, Mathematics
The basic properties of topological groups are used to prove the Fundamental Theorem of Galois Theory for arbitrary extensions and present a discussion of topological groups followed by an investigation of infinite dimensional Galois theory. Classical Galois theory is concerned with the investigation of the group of G of permutations of the roots of a polynomial equation f(x) = 0 over the field of rational numbers Q. If K is the field obtained by adjoining the roots of this polynomial to Q, then K is a finite dimensional algebraic extension of Q, and G is the group of automorphisms of K that leave each element of Q fixed.
Sundstrom, Theodore A., "Topological Groups and Infinite Dimensional Galois Theory" (1968). Honors Theses. 305.
Honors Thesis-Campus Only