UID:
almahu_9947367219502882
Format:
1 online resource (259 p.)
ISBN:
1-281-76885-5
,
9786611768850
,
0-08-087389-8
Series Statement:
Pure and applied mathematics (Academic Press) ; 73
Content:
Modular representations of finite groups
Note:
Description based upon print version of record.
,
Front Cover; Modular Representations of Finite Groups; Copyright Page; Contents; Preface; Note to the Reader; Notation; Chapter I. Representation Modules; 1.1 Group algebras and modules; 1.2 Reducible and irreducible modules; 1.3 Semisimple rings and the Wedderburn structure theorem; 1.4 Tensor products; 1.5 The number of irreducible KG-modules; 1.6 Indecomposable modules; 1.7 Absolutely indecomposable and absolutely irreducible modules; 1.8 Principal indecomposable modules; 1.9 Composition factors and intertwining numbers; 1.10 Notes and comments; Chapter II. Induced Modules and Characters
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2.1 Induced modules2.2 Clifford's theorem; 2.3 Group characters; 2.4 The theory of ordinary characters; 2.5 Induced characters; 2.6 Brauer's theorem on induced characters; 2.7 Splitting fields; 2.8 Notes and comments; Chapter III. Modular Representations and Characters; 3.1 The p-adic integers; 3.2 p-adic algebras; 3.3 Ordinary and modular representations; 3.4 Lifting idempotents; 3.5 The case where p does not divide |G|; 3.6 Modular characters; 3.7 Cartan invariants, decomposition numbers, and orthogonality relations; 3.8 Modular characters of p-solvable groups; 3.9 Notes and comments
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Chapter IV. Blocks of Group Algebras4.1 Blocks; 4.2 Classifying modules, characters, and idempotents into blocks; 4.3 Defect groups; 4.4 Further analysis of the Cartan matrix and decomposition matrix; 4.5 The characters in a block of given defect; 4.6 Blocks of small defect; 4.7 Notes and comments; Chapter V. The Theory of Indecomposable Modules; 5.1 Relatively projective modules; 5.2 Vertices and sources; 5.3 Green's theorem; 5.4 The degrees of indecomposable modules; 5.5 Vertices and defect groups; 5.6 Restriction of indecomposable modules; 5.7 Jordan's theorem in characteristic p
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5.8 Notes and commentsChapter VI. The Main Theorems of Brauer; 6.1 The Brauer homomorphism; 6.2 Blocks with normal p-subgroups; 6.3 The Brauer correspondence: The First Main Theorem; 6.4 Extension of the First Main Theorem; 6.5 Generalized decomposition numbers: The Second Main Theorem; 6.6 Principal blocks: The Third Main Theorem; 6.7 The characters in the principal block; 6.8 Notes and comments; Chapter VII. Fusion of 2-Groups; 7.1 Further results on generalized decomposition numbers; 7.2 Some technical lemmas; 7.3 Groups with Sylow 2-subgroups of type (2m, 2m)
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7.4 Groups with quaternion Sylow 2-subgroups7.5 Glauberman's Z*-theorem; 7.6 Notes and comments; Chapter VIII. Blocks with Cyclic Defect Groups; 8.1 Extending characters from normal subgroups; 8.2 Blocks with normal cyclic defect groups; 8.3 Groups with cyclic Sylow p-subgroups; 8.4 Some technical lemmas; 8.5 Groups of order g = pg0, with p X g0; 8.6 Groups with a faithful representation of degree d 〈1/2( p - 1); 8.7 Criteria for normal Sylow p-groups; 8.8 Notes and comments; References; Index
,
English
Additional Edition:
ISBN 0-12-568650-1
Language:
English
