The Representation Theory of Finite Groups (Volume 2) (North-Holland Mathematical Library, Volume 2)

Cover North-Holland Mathematical Library 25 Title Page Copyright Page Dedication Preface Contents Chapter 1 1. Preliminaries 2. Module constructions 3. Finiteness conditions 4. Projective and relatively projective modules 5. Complete reducibility 6. The radical 7. Idempotents and blocks 8. Rings of endomorphisms 9. Completeness 10. Local rings 11. Unique decompositions 12. Criteria for lifting idempotents 13. Principal indecomposable modules 14. Duality in algebras 15. Relatively injective modules for algebras 16. Algebras over fields 17. Algebras over complete local domains 18. Extensions of domains 19. Representations and traces Chapter 2 1. Group algebras 2. Modules over group algebras 3. Relative traces 4. The representation algebra of R[G] 5. Algebraic modules 6. Projective resolutions Chapter 3 1. Basic assumptions and notation 2. F[G] modules 3. Group rings over complete local domains 4. Vertices and sources 5. The Green correspondence 6. Defect groups 7. Brauer homomorphisms 8. R[G × G] modules 9. The Brauer correspondence Chapter 4 1. Characters 2. Brauer characters 3. Orthogonality relations 4. Characters in blocks 5. Some open problems 6. Higher decomposition numbers 7. Central idempotents and characters 8. Some natural mappings 9. Schur indices over Q[sub(p)] 11. Self dual modules in characteristic 2 Chapter 5 1. Some elementary results 2. Inertia groups 3. Blocks and normal subgroups 4. Blocks and quotient groups 5. Properties of the Brauer correspondence 6. Blocks and their germs 7. Isometries 9. Subsections 10. Lower defect groups 11. Groups with a given deficiency class Chapter 6 1. Blocks and extensions of R 2. Radicals and normal subgroups 3. Serial modules and normal subgroups 5. The radical of R[G] 6. p-Radical groups Chapter 7 1. Blocks with a cyclic defect group 2. Statements of results 3. Some preliminary results 4. Proofs of (2.1)–(2.10) 6. The Brauer tree 7. Proofs of (2.11)–(2.19) 8. Proofs of (2.20)–(2.25) 9. Some properties of the Brauer tree 10. Some consequences 11. Some examples 14. The Brauer tree and field extensions 15. Irreducible modules with a cyclic vertex Chapter 8 1. Groups with a Sylow group of prime order 3. Groups of type L[sub(2)](p) 4. A characterization of some groups 5. Some consequences of (4.1) 6. Permutation groups of prime degree 7. Characters of degree less than p – 1 8. Proof of (7.1) 9. Proof of (7.2) 10. Proof of (7.3) 11. Some properties of permutation groups 12. Permutation groups of degree 2p 13. Characters of degree p Chapter 9 1. The structure of A(G) 2. A(G) in case a S[sub(p)]-group of G is cyclic and R is a field 3. Permutation modules 4. Endo-permutation modules for p-groups Chapter 10 1. Groups with a normal p'-subgroup 2. Brauer characters of p-solvable groups 3. Principal indecomposable characters of p-solvable groups 4. Blocks of p-solvable groups 5. Principal series modules for p-solvable groups 6. The problems of Chapter 4, section 5 for p-solvable groups 7. Irreducible modules of p-solvable groups 8. Isomorphic blocks Chapter 11 1. An analogue of Jordan's theorem Chapter 12 1. Types of blocks 2. Some properties of the principal block 3. Involutions and blocks 4. Some computations with columns 5. Groups with an abelian S[sub(2)]-group of type (2[sup(m)], 2[sup(m)]) 6. Blocks with special defect groups 7. Groups with a quaternion S[sub(2)]-group 8. The Z*-theorem Bibliography Subject Index