Representations and Characters of Groups
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BeschreibungThis is the second edition of the popular textbook on representation theory of finite groups. The authors have revised the text greatly and included new chapters on Characters of GL(2, q) and Permutations and Characters. The theory is developed in terms of modules, since this is appropriate for more advanced work, but considerable emphasis is placed upon constructing characters. The character tables of many groups are given, including all groups of order less than 32, and all but one of the simple groups of order less than 1000. Each chapter is accompanied by a variety of exercises, and full solutions to all the exercises are provided at the end of the book.
Inhaltsverzeichnis1. Groups and homomorphisms; 2. Vector spaces and linear transformations; 3. Group representations; 4. FG-modules; 5. FG-submodules; 6. Group algebras; 7. FG-homomorphisms; 8. Mashcke's theorem; 9. Schur's lemma; 10. Irreducible modules and the group algebra; 11. More on the group algebra; 12. Conjugacy classes; 13. Characters; 14. Inner products of characters; 15. The number of irreducible characters; 16. Character tables and orthogonality relations; 17. Normal subgroups and lifted characters; 18. Some elementary character tables; 19. Tensor products; 20. Restriction to a subgroup; 21. Induced modules and characters; 22. Algebraic integers; 23. Real representations; 24. Summary of properties of character tables; 25. Characters of groups of order pq; 26. Characters of some p-groups; 27. Character table of the simple group of order 168; 28. Character table of GL(2,q); 29. Permutations and characters; 30. Applications to group theory; 31. Burnside's theorem; 32. An application of representation theory to molecular vibration.
Pressestimmen'... this reviewer regards the second printing of the book as a gem in studying representation theory of finite groups.' R. W. van der Wall, Zentralblatt fur Mathematik 'This is a beautiful well-balanced introduction to representations and characters of finite groups over the complex field, suitable for advanced undergraduate and beginning graduate students. The reviewer enjoyed the exposition tremendously and strongly recommends this already popular book both as a textbook and for self-study.' EMS 'For me, the attractive features are the short chapters (substantial but bite-sized), the motivational comments throughout the book and useful summaries at the end of each chapter, the wealth of detailed examples which break up and illuminate the theory, and full solutions to all the exercises.' The Mathematical Gazette 'The review found this to be a clearly and carefully written book, which he will recommend to all students seeking an introduction to group representation theory. the authors write in a down-to-earth style, provide a large number of examples throughout, and give very useful content summaries at the end of each chapter ... In summary, the additions to the second edition only improve what was already an excellent text.' Proceedings of the Edinburgh Mathematical Society
Untertitel: 2 Rev ed. 28 b/w illus. 163 tables. Sprache: Englisch.
Verlag: Cambridge University Press
Erscheinungsdatum: Oktober 2001
Seitenanzahl: 468 Seiten