Algebra II

3 credits · Undergraduate Programs

An intermediate course in the theory of groups and fields. Group theory: group actions, Sylow theorems, solvable, nilpotent and p-groups, simplicity of alternating groups and PSL(n,q). Field theory: algebraic and transcendental extensions, separability and normality, Galois theory, insolvability of the general quintic equation, and computation of Galois groups over the rationals. Prerequisite(s): Mathematics 315; and Mathematics 311.