Excellent text approaches characters via rings (or algebras). In addition to techniques for applying characters to "pure" group theory, much of the book focuses on properties of the characters themselves and how these properties reflect and are reflected in the structure of the group. "A pleasure to read." — American Mathematical Society. 1976 edition.
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15 of 18 people found the following review helpful:
3.0 out of 5 stars
Not clear for beginners,
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This review is from: Character Theory of Finite Groups (Dover Books on Mathematics) (Paperback)
Though Robert Greiss (of the Monster group fame) has assured me that the proofs and theory in the book are all sound, a beginner would have a difficult time believing it. The proofs generally leave a great deal to be proved, and worse to not point out these short comings so that a reader could at least work them out on the side. I am sure that if one understands representation theory then this is a marvelous reference, but for beginners I prefer Curtis & Reiner's Methods of Representation Theory Volume 1, or even the last section of Dummit and Foote's Abstract Algebra which is the best explained intro to representation and character theory that I have found.
3 of 4 people found the following review helpful:
5.0 out of 5 stars
An excellent book on character theory,
This review is from: Character Theory of Finite Groups (Dover Books on Mathematics) (Paperback)
This classic book offers one of the definite treatments of character theory of finite groups, written by one of the foremost experts in the field. The text assumes that the reader had been exposed to a one year sequence of graduate level algebra course (knowledge about the basics of the theory of finite groups is necessary to read this book; for example, the book "Groups and Representations" by Alperin and Bell provides the necessary background material).
The book is densely written and contains an incredible amount of material. The author provides concise but very readable proofs. Each chapter contains a large number of exercises that help the reader to master the material. The enormous coverage of material makes this book one of the most useful references on (ordinary) characters of finite groups.
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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44
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- Finite Groups 2003: Proceedings Of The Gainesville Conference On Finite Groups, March 6 - 12, 2003 ([De Gruyter Proceedings in Mathematics]) by Finite Groups 200 on 4 pages
- Representations of Solvable Groups (London Mathematical Society Lecture Note Series) by Olaf Manz in Front Matter, and Back Matter
- Ischia Group Theory 2004: Proceedings of a Conference in Honor of Marcel Herzog, March 31-april 3, 2004, Naples, Italy (Contemporary Mathematics) by Bianchi, Herfort, Longobardi, Maj & Scoppola Arad on page 93, and page 141
- Enumerative Combinatorics, Volume 2 by Richard P. Stanley on page 522, and page 538
- Groups St Andrews 2001 in Oxford: Volume 2 (London Mathematical Society Lecture Note Series) by C. M. Campbell on page 125, and page 225
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