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.
→ STARS müfredatı (resmi syllabus)
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Course Learning Outcomes: Course Learning Outcome Assessment Understand and apply key group-theoretic tools such as group actions, p-groups, Sylow theorems, and the Frattini argument. Midterm Homework Analyze solvable finite group structures using Hall subgroups, Carter subgroups and Schur-Zassenhaus theorem. Midterm Final Homework Investigate group structure by the fusion theory. Final Homework