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Character Theory of Finite Groups"The book is a pleasure to read. There is no question but that it will become, and deserves to be, a widely used textbook and reference." Bulletin of the American Mathematical Society. Character theory provides a powerful tool for proving theorems about finite groups. In addition to dealing with techniques for applying characters to "pure" group theory, a large part of this book is devoted to the properties of the characters themselves and how these
"The book is a pleasure to read. There is no question but that it will become, and deserves to be, a widely used textbook and reference." -- Bulletin of the American Mathematical Society.Character theory provides a powerful tool for proving theorems about finite groups. In addition to dealing with techniques for applying characters to "pure" group theory, a large part of this book is devoted to the properties of the characters themselves and how these properties reflect and are reflected in the structure of the group.
Chapter I consists of ring theoretic preliminaries. Chapters 2 to 6 and 8 contain the basic material of character theory, while Chapter 7 treats an important technique for the application of characters to group theory. Chapter 9 considers irreducible representations over arbitrary fields, leading to a focus on subfields of the complex numbers in Chapter 10. In Chapter 15 the author introduces Brauer's theory of blocks and "modular characters." Remaining chapters deal with more specialized topics, such as the connections between the set of degrees of the irreducible characters and structure of a group. Following each chapter is a selection of carefully thought out problems, including exercises, examples, further results and extensions and variations of theorems in the text.
Prerequisites for this book are some basic finite group theory: the Sylow theorems, elementary properties of permutation groups and solvable and nilpotent groups. Also useful would be some familiarity with rings and Galois theory. In short, the contents of a first-year graduate algebra course should be sufficient preparation.
Binding Type: Paperback
Publisher: Dover Publications
Published: 11/02/2011
ISBN: 9780486680149
Pages: 336
Weight: 0.76lbs
Size: 8.48h x 5.42w x 0.63d
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Succinct and Spot on
Format: Perfect Paperback
This is a fantastic little book and much needed. A youth discussion group met and we used this book as the basis for the topic of disagreeing to the glory of God. I heard multiple ways students had applied it in their contexts at home and school. Gavin should be glad to know it has made a difference.
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Reviewed in the United States on November 7, 2025
★★★★★ 4
The Art of Disagreeing
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I'm currently reading this book. So far it's been informative and supportive.
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Reviewed in the United States on April 10, 2025
★★★★★ 5
Great read
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Good book
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Reviewed in the United States on June 1, 2026
★★★★★ 5
Great Read
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A great addition to the original the "5 Love Language". Will definitely give you better insight to your partners love language.
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Reviewed in the United States on April 30, 2026
★★★★★ 5
Great book to read
Format: Paperback
If you want to learn about love languages, it’s an excellent book. It really makes a lot of sense.
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Reviewed in the United States on March 18, 2026