Hardcover ISBN:  9780821842294 
Product Code:  CHEL/359.H 
List Price:  $69.00 
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AMS Member Price:  $62.10 
eBook ISBN:  9781470430351 
Product Code:  CHEL/359.H.E 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $58.50 
Hardcover ISBN:  9780821842294 
eBook: ISBN:  9781470430351 
Product Code:  CHEL/359.H.B 
List Price:  $134.00 $101.50 
MAA Member Price:  $120.60 $91.35 
AMS Member Price:  $120.60 $91.35 
Hardcover ISBN:  9780821842294 
Product Code:  CHEL/359.H 
List Price:  $69.00 
MAA Member Price:  $62.10 
AMS Member Price:  $62.10 
eBook ISBN:  9781470430351 
Product Code:  CHEL/359.H.E 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $58.50 
Hardcover ISBN:  9780821842294 
eBook ISBN:  9781470430351 
Product Code:  CHEL/359.H.B 
List Price:  $134.00 $101.50 
MAA Member Price:  $120.60 $91.35 
AMS Member Price:  $120.60 $91.35 

Book DetailsAMS Chelsea PublishingVolume: 359; 1976; 303 ppMSC: Primary 20
Character theory is a powerful tool for understanding finite groups. In particular, the theory has been a key ingredient in the classification of finite simple groups. Characters are also of interest in their own right, and their properties are closely related to properties of the structure of the underlying group.
The book begins by developing the module theory of complex group algebras. After the moduletheoretic foundations are laid in the first chapter, the focus is primarily on characters. This enhances the accessibility of the material for students, which was a major consideration in the writing. Also with students in mind, a large number of problems are included, many of them quite challenging.
In addition to the development of the basic theory (using a cleaner notation than previously), a number of more specialized topics are covered with accessible presentations. These include projective representations, the basics of the Schur index, irreducible character degrees and group structure, complex linear groups, exceptional characters, and a fairly extensive introduction to blocks and Brauer characters.
This is a corrected reprint of the original 1976 version, later reprinted by Dover. Since 1976 it has become the standard reference for character theory, appearing in the bibliography of almost every research paper in the subject. It is largely selfcontained, requiring of the reader only the most basic facts of linear algebra, group theory, Galois theory and ring and module theory.
ReadershipGraduate students and research mathematicians interested in finite groups, character theory, and representation theory.

Table of Contents

Chapters

Chapter 1. Algebras, modules, and representations

Chapter 2. Group representations and characters

Chapter 3. Characters and integrality

Chapter 4. Products of characters

Chapter 5. Induced characters

Chapter 6. Normal subgroups

Chapter 7. T.I. sets and exceptional characters

Chapter 8. Brauer’s theorem

Chapter 9. Changing the field

Chapter 10. The Schur index

Chapter 11. Projective representations

Chapter 12. Character degrees

Chapter 13. Character correspondence

Chapter 14. Linear groups

Chapter 15. Changing the characteristic

Appendix. Some character tables


Additional Material

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Character theory is a powerful tool for understanding finite groups. In particular, the theory has been a key ingredient in the classification of finite simple groups. Characters are also of interest in their own right, and their properties are closely related to properties of the structure of the underlying group.
The book begins by developing the module theory of complex group algebras. After the moduletheoretic foundations are laid in the first chapter, the focus is primarily on characters. This enhances the accessibility of the material for students, which was a major consideration in the writing. Also with students in mind, a large number of problems are included, many of them quite challenging.
In addition to the development of the basic theory (using a cleaner notation than previously), a number of more specialized topics are covered with accessible presentations. These include projective representations, the basics of the Schur index, irreducible character degrees and group structure, complex linear groups, exceptional characters, and a fairly extensive introduction to blocks and Brauer characters.
This is a corrected reprint of the original 1976 version, later reprinted by Dover. Since 1976 it has become the standard reference for character theory, appearing in the bibliography of almost every research paper in the subject. It is largely selfcontained, requiring of the reader only the most basic facts of linear algebra, group theory, Galois theory and ring and module theory.
Graduate students and research mathematicians interested in finite groups, character theory, and representation theory.

Chapters

Chapter 1. Algebras, modules, and representations

Chapter 2. Group representations and characters

Chapter 3. Characters and integrality

Chapter 4. Products of characters

Chapter 5. Induced characters

Chapter 6. Normal subgroups

Chapter 7. T.I. sets and exceptional characters

Chapter 8. Brauer’s theorem

Chapter 9. Changing the field

Chapter 10. The Schur index

Chapter 11. Projective representations

Chapter 12. Character degrees

Chapter 13. Character correspondence

Chapter 14. Linear groups

Chapter 15. Changing the characteristic

Appendix. Some character tables