Finite Group Theory

MATH 529 is a graduate deep-dive into the structural machinery that lets you take a finite group apart and see why it has to look the way it does, Sylow theory and group actions are just the entry point, with most of the semester spent on nilpotent and solvable structure, coprime actions, and the local-to-global bridge that fusion and transfer provide. You work through this almost entirely via problem sets out of Isaacs and Kurzweil-Stellmacher, with one midterm and a final to make sure the proofs actually stick. It assumes you're comfortable with undergraduate algebra at the level of a first group theory course, and it's the standard prerequisite vocabulary for representation theory, cohomology of groups, and the local analysis that shows up in the classification of finite simple groups.