Title
Character Theory of Finite Groups (Dover Books on Mathematics),Used
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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 Brauers 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 firstyear graduate algebra course should be sufficient preparation.
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- Q: What is the main focus of 'Character Theory of Finite Groups'? A: The book primarily focuses on character theory as a tool for understanding and proving theorems about finite groups, covering both techniques and properties of characters.
- Q: What prerequisites are needed for this book? A: A basic understanding of finite group theory is required, including knowledge of Sylow theorems, permutation groups, and familiarity with rings and Galois theory.
- Q: Who is the author of this book? A: The author of 'Character Theory of Finite Groups' is I. Martin Isaacs.
- Q: How many pages does the book have? A: The book contains 336 pages.
- Q: What type of binding does this book have? A: This edition is available in paperback binding.
- Q: When was 'Character Theory of Finite Groups' published? A: The book was published on November 2, 2011.
- Q: What topics are covered in this book? A: The book covers ring theoretic preliminaries, basic materials of character theory, irreducible representations, Brauer's theory of blocks, and specialized topics related to group structure.
- Q: Is this book suitable for beginners in group theory? A: While the book assumes some prior knowledge, it can be beneficial for graduate students who have completed a first-year algebra course.
- Q: What is the significance of character theory in group theory? A: Character theory is significant as it provides powerful methods for analyzing the structure of finite groups through the properties of their characters.
- Q: Does the book include exercises or problems? A: Yes, each chapter includes carefully thought-out problems, exercises, examples, and further results related to the theorems discussed.