Free Delivery Over $100
|
|
|||
|
||||
Overview""""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. Full Product DetailsAuthor: I. Martin IsaacsPublisher: Dover Publications Inc. Imprint: Dover Publications Inc. Dimensions: Width: 13.50cm , Height: 1.70cm , Length: 21.50cm Weight: 0.360kg ISBN: 9780486680149ISBN 10: 0486680142 Pages: 336 Publication Date: 28 March 2003 Audience: General/trade , General Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsPreface; Acknowledgments; Notation 1. Algebras, modules, and representations. Problems 2. Group representations and characters. Problems 3. Characters and integrality. Problems 4. Products of characters. Problems 5. Induced characters. Problems 6. Normal subgroups. Problems 7. T.I. sets and exceptional characters. Problems 8. Brauer's theorem. Problems 9. Changing the field. Problems 10. The Schur index. Problems 11. Projective representations. Problems 12. Character degrees. Problems 13. Character correspondence. Problems 14. Linear groups. Problems 15. Changing the characteristic. Problems Appendix. Some character tables Biographic notes; References; IndexReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
||||
