Cohomology of groups, crossed products, and an introduction to spectral sequences.
Presentations, the Nielsen-Schreier theorem, and the Kurosh theorem. Chapter C-2: Representation Theory 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: Cohomology of groups, crossed products, and an introduction
Proofs for theorems by Burnside and Frobenius. Chapter C-3: Homology Cohomology of groups
Fundamental structures for homological algebra. Sheaves: An introduction to sheaves and sheaf cohomology. K-Theory: Specifically focusing on the functors K0cap K sub 0 G0cap G sub 0 Chapter C-5: Commutative Rings III Advanced topics in commutative algebra:
Introduces homological algebra and its applications to groups:
Characterization and finitely generated modules over Dedekind rings.