UID:
almahu_9947367879002882
Format:
1 online resource (517 p.)
ISBN:
1-282-03484-7
,
9786612034848
,
0-08-096013-8
Series Statement:
North-Holland mathematical library ; v. 25
Content:
The Representation Theory of Finite Groups
Note:
Includes index.
,
Front Cover; The Representation Theory of Finite Groups; Copyright Page; Contents; Preface; Chapter I; 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
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5. Some open problems6. Higher decomposition numbers; 7. Central idempotents and characters; 8. Some natural mappings; 9. Schur indices over Qp; 10. The ring A0z(R[G]); 11. Self dual modules in characteristic 2; Chapter V; 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; 8. p-heights; 9. Subsections; 10. Lower defect groups; 11. Groups with a given deficiency class; Chapter VI; 1. Blocks and extensions of R; 2. Radicals and normal subgroups
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3. Serial modules and normal subgroups4. The radical of R [G]; 5. The radical of R [GI; 6. p-Radical groups; Chapter VII; 1. Blocks with a cyclic defect group; 2. Statements of results; 3. Some preliminary results; 4. Proofs of (2.1)-(2.10); 5. Proofs of (2.11)-(2.17) in case K = K; 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; 12. The indecomposable R [GI modules in B; 13. Schur indices of irreducible characters in B; 14. The Brauer tree and field extensions
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15. Irreducible modules with a cyclic vertexChapter VIII; 1. Groups with a Sylow group of prime order; 2. Tensor products of R[N] modules; 3. Groups of type L2(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 IX; 1. The structure of A (G); 2. A (G) in case a Sp-group of G is cyclic and R is a field
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3. Permutation modules
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English
Additional Edition:
ISBN 0-444-86155-6
Language:
English
