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Representation Theory of Finite Groups
- 1st Edition - January 1, 1965
- Author: Martin Burrow
- Language: English
- eBook ISBN:9 7 8 - 1 - 4 8 3 2 - 5 8 2 1 - 8
Representation Theory of Finite Groups is a five chapter text that covers the standard material of representation theory. This book starts with an overview of the basic concepts… Read more
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Request a sales quoteRepresentation Theory of Finite Groups is a five chapter text that covers the standard material of representation theory. This book starts with an overview of the basic concepts of the subject, including group characters, representation modules, and the rectangular representation. The succeeding chapters describe the features of representation theory of rings with identity and finite groups. These topics are followed by a discussion of some of the application of the theory of characters, along with some classical theorems. The last chapter deals with the construction of irreducible representations of groups. This book will be of great value to graduate students who wish to acquire some knowledge of representation theory.
Preface
Chapter I. Foundations
1. Introduction
2. Group Characters
3. Representation Modules
4. Application of Ideas and Results from Group Theory
5. The Regular Representation
Exercises
Chapter II. Representation Theory of Rings with Identity
6. Some Fundamental Lemmas
Exercise
7. The Principal Indecomposable Representations
8. The Radical of a Ring
9. Semisimple Rings
10. The Wedderburn Structure Theorems for Semisimple Rings
11. Intertwining Numbers
12. Multiplicities of the Indecomposable Representation
13. The Generalized Burnside Theorem
Exercises
Chapter III. The Representation Theory of Finite Groups
14· The Group Algebra
15. The Regular Representation of a Group
16. Semisimplicity of the Group Algebra
17. The Center of the Group Algebra
18. The Number of Inequivalent Irreducible Representations
19. Relations on the Irreducible Characters
20. The Module of Characters over the Integers
21. The Kronecker Product of Two Representations
Exercises
22. Linear Characters
Exercises
23. Induced Representations and Induced Characters
Exercises
Chapter IV. Applications of the Theory of Characters
24. Algebraic Numbers
25. Some Results from the Theory of Characters
26. Normal Subgroups and the Character Table
A. The Existence of Normal Subgroups
B. The Determination of All Normal Subgroups
27. Some Classical Theorems
Exercises
Chapter V. The Construction of Irreducible Representations
28. Primitive Idempotents
29. Some examples of Group Representations
1. Cyclic Groups
2. Abelian Groups
3. The Symmetric Groups Sn
Exercises
Chapter VI. Modular Representations
30. General Remarks
31. p-Regular Elements of a Finite Group
32. Conditions for Two Representations to Have the Same Composition Factors
33. The Brauer Characters
34. Integral Representations
Exercise
35. Ordinary and Modular Representations of Algebras
1. Arithmetic in an Algebra
Exercise
2. Connection with Integral Representations
36. p-Adic Fields
1. General Definition and Properties
2. Ordinary Valuation Metrical Properties
3. Completion of a p-Adic Field
4. p-Adic Valuation of the Rational Field
5. Extension of the p-Adic Valuation to Algebraic Number Fields
37. Algebras over a p-Adic Field
1. Notation
2. Preliminary Results
38. A Connection between the Intertwining Numbers
39. Modular Representations of Groups
40. Cartan Invariants and Decomposition Numbers
41. Character Relations
42. Modular Orthogonality Relations
Appendix
1. Groups
2. Rings, Ideals, and Fields
Bibliograpy
Subject Index
- No. of pages: 196
- Language: English
- Edition: 1
- Published: January 1, 1965
- Imprint: Academic Press
- eBook ISBN: 9781483258218
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