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Character Theory of Finite Groups
 
I. Martin Isaacs University of Wisconsin, Madison, Madison, WI
Character Theory of Finite Groups
AMS Chelsea Publishing: An Imprint of the American Mathematical Society
Hardcover ISBN:  978-0-8218-4229-4
Product Code:  CHEL/359.H
List Price: $69.00
MAA Member Price: $62.10
AMS Member Price: $62.10
eBook ISBN:  978-1-4704-3035-1
Product Code:  CHEL/359.H.E
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $58.50
Hardcover ISBN:  978-0-8218-4229-4
eBook: ISBN:  978-1-4704-3035-1
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
Character Theory of Finite Groups
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Character Theory of Finite Groups
I. Martin Isaacs University of Wisconsin, Madison, Madison, WI
AMS Chelsea Publishing: An Imprint of the American Mathematical Society
Hardcover ISBN:  978-0-8218-4229-4
Product Code:  CHEL/359.H
List Price: $69.00
MAA Member Price: $62.10
AMS Member Price: $62.10
eBook ISBN:  978-1-4704-3035-1
Product Code:  CHEL/359.H.E
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $58.50
Hardcover ISBN:  978-0-8218-4229-4
eBook ISBN:  978-1-4704-3035-1
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 Details
     
     
    AMS Chelsea Publishing
    Volume: 3591976; 303 pp
    MSC: 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 module-theoretic 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 self-contained, requiring of the reader only the most basic facts of linear algebra, group theory, Galois theory and ring and module theory.

    Readership

    Graduate 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
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 3591976; 303 pp
MSC: 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 module-theoretic 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 self-contained, requiring of the reader only the most basic facts of linear algebra, group theory, Galois theory and ring and module theory.

Readership

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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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