MATH 429 takes the basic group theory you saw in abstract algebra and pushes it into the structural machinery working mathematicians actually use: Sylow analysis, nilpotent and solvable decompositions, coprime actions, and the transfer-and-fusion toolkit that controls how p-subgroups sit inside a finite group. Work is theorem-driven — you'll spend the semester proving things on homeworks and two exams, gradually building from group actions up to results like Schur-Zassenhaus, Burnside's fusion theorem, and the classification of Frobenius groups. It's a natural follow-up to a first algebra course and the standard on-ramp for anyone heading toward representation theory, cohomology of groups, or research in algebra.
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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