Customer Reviews

Character Theory of Finite Groups (Dover Books on Mathematics)

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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.

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.