Presentations, the Nielsen-Schreier theorem, and the Kurosh theorem. Chapter C-2: Representation Theory
Hilbert's syzygy theorem and regular local rings. 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: the Nielsen-Schreier theorem
Introduces homological algebra and its applications to groups: Advanced Modern Algebra: Third Edition, Part 2 ...
Focuses on the theory of modules and group representations, primarily in the semisimple case:
Orthogonality relations, character tables, and induced characters.
Structural analysis of these group types. Projective Groups: Simplicity of and projective unimodular groups.