Focuses on the theory of modules and group representations, primarily in the semisimple case:
Part 2 of Joseph J. Rotman's (Graduate Studies in Mathematics, Volume 180) focuses on advanced graduate-level topics, building on the foundational concepts introduced in Part 1. The book is organized into five primary chapters: Chapter C-1: More Groups Advanced Modern Algebra: Third Edition, Part 2 ...
Complexes, homology functors, and derived functors including Ext and Tor. Chapter C-4: More Categories Extends the category theory introduced in Part 1: Focuses on the theory of modules and group
Proofs for theorems by Burnside and Frobenius. Chapter C-3: Homology Chapter C-4: More Categories Extends the category theory
Orthogonality relations, character tables, and induced characters.
This chapter covers group theory in greater depth, including: Actions on graphs and counting principles. Sylow Theorems: Detailed exploration of Sylow theory.
Presentations, the Nielsen-Schreier theorem, and the Kurosh theorem. Chapter C-2: Representation Theory