Representations and Characters of Groups

Author: Gordon James,Martin W. Liebeck,Martin Liebeck

Publisher: Cambridge University Press

ISBN: 9780521003926

Category: Mathematics

Page: 458

View: 729

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Introducing the representation theory of finite groups, this second edition has been revised and updated. The theory is developed in terms of modules with considerable emphasis placed upon constructing characters.
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Representations and Characters of Groups

Author: Gordon Douglas James,Martin W. Liebeck

Publisher: N.A

ISBN: 9780521445900

Category: Representations of groups

Page: 419

View: 1302

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This book provides a modern introduction to the representation theory of finite groups. 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. Amongst those applications covered are Burnside's paqb theorem, the use of character theory in studying subgroup structure, and a description of how to use representation theory to investigate molecular vibration. Each chapter is accompanied by a variety of exercises, and full solutions to all the exercises are provided at the end of the book. This will be suitable as a text for those teaching a course in representation theory, and in view of the applications of the subject, will be of interest to chemists and physicists as well as mathematicians.
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Representations and Characters of Finite Groups

Author: M. J. Collins,Dr Michael J Collins, M.D,Michael J. Stratford-Collins

Publisher: Cambridge University Press

ISBN: 9780521234405

Category: Mathematics

Page: 242

View: 6784

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Representation theory and character theory have proved essential in the study of finite simple groups since their early development by Frobenius. The author begins by presenting the foundations of character theory in a style accessible to advanced undergraduates that requires only a basic knowledge of group theory and general algebra. This theme is then expanded in a self-contained account providing an introduction to the application of character theory to the classification of simple groups. The book follows both strands of the theory: the exceptional characteristics of Suzuki and Feit and the block character theory of Brauer and includes refinements of original proofs that have become available as the subject has grown.
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The Theory of Group Characters and Matrix Representations of Groups

Author: Dudley Ernest Littlewood

Publisher: American Mathematical Soc.

ISBN: 9780821874356

Category: Mathematics

Page: 310

View: 721

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Originally written in 1940, this book remains a classical source on representations and characters of finite and compact groups. The book starts with necessary information about matrices, algebras, and groups. Then the author proceeds to representations of finite groups. Of particular interest in this part of the book are several chapters devoted to representations and characters of symmetric groups and the closely related theory of symmetric polynomials. The concluding chapterspresent the representation theory of classical compact Lie groups, including a detailed description of representations of the unitary and orthogonal groups. The book, which can be read with minimal prerequisites (an undergraduate algebra course), allows the reader to get a good understanding ofbeautiful classical results about group representations.
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Groups and Characters

Author: Victor E Hill

Publisher: CRC Press

ISBN: 1351443801

Category: Mathematics

Page: 239

View: 646

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Group representation theory is both elegant and practical, with important applications to quantum mechanics, spectroscopy, crystallography, and other fields in the physical sciences. Until now, however, there have been virtually no accessible treatments of group theory that include representations and characters. The classic works in the field require a high level of mathematical sophistication, and other texts omit representations and characters. Groups and Characters offers an easy-to-follow introduction to the theory of groups and of group characters. Designed as a rapid survey of the subject, this unique text emphasizes examples and applications of the theorems, and avoids many of the longer and more difficult proofs. The author presents group theory through the Sylow Theorems and includes the full subgroup structure of A5. Representations and characters are worked out with numerous character tables, along with real and induced characters that lead to the table for S5. The text includes specific sections that provide the mathematical basis for some of the important applications of group theory in spectroscopy and molecular structure. It also offers numerous exercises-some stressing computation of concrete examples, others stressing development of the mathematical theory. Groups and Characters provides the ideal grounding for more advanced studies with the classic texts, and for more broad-based work in abstract algebra. Furthermore, physical scientists-whose experience with groups and characters may not be rigorous-will find Groups and Characters the ideal means for gaining a sense of the mathematics lying behind the techniques used in applications.
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Character Theory of Finite Groups

Author: Bertram Huppert

Publisher: Walter de Gruyter

ISBN: 3110809230

Category: Mathematics

Page: 624

View: 5371

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The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany
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Representation Theory of Finite Groups

Author: Martin Burrow

Publisher: Courier Corporation

ISBN: 0486145077

Category: Mathematics

Page: 208

View: 7606

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DIVConcise, graduate-level exposition covers representation theory of rings with identity, representation theory of finite groups, more. Exercises. Appendix. 1965 edition. /div
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Character Theory of Finite Groups

Author: I. Martin Isaacs

Publisher: Courier Corporation

ISBN: 9780486680149

Category: Mathematics

Page: 303

View: 852

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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 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.
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