Algebra II

Galois Theory Field Extensions Splitting Fields Galois Groups of Polynomials Solvability by Radicals Cyclotomic Fields Finite Fields Irreducible Polynomials Polynomial Rings and Prime Ideals Finite Group Theory Free Groups and Group Presentations Sylow Theorems Simple Groups Classification of Finite Groups p-Groups Solvable Groups Normal Subgroups and Commutator Subgroups Abelian Groups and Direct Sum Decompositions Symmetric and Alternating Groups Representation Theory Character Theory