**AMS Chelsea Publishing**

Volume: 359;
1976;
303 pp;
Hardcover

MSC: Primary 20;

**Print ISBN: 978-0-8218-4229-4
Product Code: CHEL/359.H**

List Price: $53.00

AMS Member Price: $47.70

MAA Member Price: $47.70

**Electronic ISBN: 978-1-4704-3035-1
Product Code: CHEL/359.H.E**

List Price: $50.00

AMS Member Price: $45.00

MAA Member Price: $45.00

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#### Supplemental Materials

# Character Theory of Finite Groups

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*I. Martin Isaacs*

AMS Chelsea Publishing: An Imprint of the American Mathematical Society

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

# Table of Contents

## Character Theory of Finite Groups

- Cover Cover11
- Title page iii4
- Contents v6
- Preface vii8
- Acknowledgments ix10
- Notation xi12
- Algebras, modules, and representations 114
- Group representations and characters 1326
- Characters and integrality 3346
- Products of characters 4760
- Induced characters 6275
- Normal subgroups 7891
- T.I. sets and exceptional characters 99112
- Brauer’s theorem 126139
- Changing the field 144157
- The Schur index 160173
- Projective representations 174187
- Character degrees 198211
- Character correspondence 219232
- Linear groups 240253
- Changing the characteristic 262275
- Appendix. Some character tables 287300
- Bibliographic notes 292305
- References 295308
- Index 297310
- Back Cover Back Cover1322