Finite Group Algebras and their Modules

Preface; Part I. The Structure of Group Algebras: 1. Idempotents in rings. Liftings; 2. Projective and injective modules; 3. The radical and artinian rings; 4. Cartan invariants and blocks; 5. Finite dimensional algebras; 6. Duality; 7. Symmetry; 8. Loewy series and socle series; 9. The p. i. m.'s; 10. Ext; 11. Orders; 12. Modular systems and blocks; 13. Centers; 14. R-forms and liftable modules; 15. Decomposition numbers and Brauer characters; 16. Basic algebras and small blocks; 17. Pure submodules; 18. Examples; Part II. Indecomposable Modules and Relative Projectivity: 1. The trace map and the Nakayama relations; 2. Relative projectivity; 3. Vertices and sources; 4. Green Correspondence; 5. Relative projective homomorphisms; 6. Tensor products; 7. The Green ring; 8. Endomorphism rings; 9. Almost split sequences; 10. Inner products on the Green ring; 11. Induction from normal subgroups; 12. Permutation models; 13. Examples; Part III. Block Theory: 1. Blocks, defect groups and the Brauer map; 2. Brauer's First Main Theorem; 3. Blocks of groups with a normal subgroup; 4. The Extended First main Theorem; 5. Defect groups and vertices; 6. Generalized decomposition numbers; 7. Subpairs; 8. Characters in blocks; 9. Vertices of simple modules; 10. Defect groups; Appendices; References; Index.