Background
Isaacs, I. Martin was born on April 14, 1940 in New York City. Son of Andrew and Lillian (Ocko) Isaacs.
(Character theory is a powerful tool for understanding fin...)
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.
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(Isaacs' love for algebra and his more than 25 years of te...)
Isaacs' love for algebra and his more than 25 years of teaching experience in mathematics is evident throughout the book. In order to draw students into the material, Isaacs offers numerous examples and exercises and he seldom teaches a definition unless it leads to some interesting or exciting theorem. A number of specialized topics are included, so professors may design a course that is compatible with their own tastes. Students using this book should have knowledge of the basic ideas of group theory, ring theory, and field theory. They should know elementary linear algebra and matrix theory and they should be comfortable with mathematical proofs (how to read them, invent them, and write them).
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Isaacs, I. Martin was born on April 14, 1940 in New York City. Son of Andrew and Lillian (Ocko) Isaacs.
Bachelor of Science, Polytech. Institute Brooklyn, 1960; Doctor of Philosophy, Harvard University, 1964.
Instructor, University of Chicago, 1966-1968; visiting assistant professor, University of Chicago, 1968-1969; associate professor, University of Wisconsin, Madison, 1979-1971; professor, University of Wisconsin, Madison, since 1971. Visiting fellow Oxford (England) University, 1984. Visiting professor University of California, Berkeley, 1988.
(Isaacs' love for algebra and his more than 25 years of te...)
(Character theory is a powerful tool for understanding fin...)
(New)
Sloan Foundation fellow, 1972.