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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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★★★★★ 5
Great spiritual guide
It’s a fairly confusing book if you don’t know a lot about the Orthodox Church. But for anyone with enough patience to want to learn how to grow spiritually this is perfect.
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Reviewed in the United States on July 30, 2025
★★★★★ 4
Will lead you on the good path
Format: Paperback
I’ve barely made my way through the rungs of the ladder, but this book is definitely one of the greater books I’ve read, however I will say that people are right when they say this specific copy has a quite a few spelling errors, but I’m personally able to manage it well. I must warn you though, THIS IS NOT A LIGHT READ, if you’re looking for something simple to learn from, look elsewhere. This book isn’t an easy pill to swallow if you’re not open minded and at least somewhat familiar with the theology of the early church fathers, however if you are, I highly recommend you give this a read if you haven’t already. Once again, a fantastic read, but read at your own discretion.
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Reviewed in the United States on May 13, 2022
★★★★★ 5
God is love. Climb the ladder.
Format: Kindle
John of the ladder. Climb it with Climacus. There are 30 rungs to ascend. Read this book and climb today.
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Reviewed in the United States on August 27, 2025
★★★★★ 5
Excellent Guide for the Soul and the Spiritual Journey
This book was one that I somehow decided upon--seemed like divine providence. For the book ended up being quite pivotal for this point in my spiritual journey. I found it very readable, loved Climacus' to-the-point style but with yet eloquent presentation. A friend who is 87 and reads books with me, across the miles, loved this book, also. It is a kind of a guidebook for the soul, step by step. The translation is excellent; the introduction quite helpful, too. I bought the book used online, and rather than resell it, this book is definitely staying in my possession so that I can refer back to it. Excellent!
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Reviewed in the United States on April 25, 2015
★★★★★ 5
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Reviewed in the United States on November 8, 2025