On Characters Of Finite Groups

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Character Theory Of Finite Groups

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Author : I. Martin Isaacs
language : en
Publisher: American Mathematical Soc.
Release Date : 2006-11-21

Character Theory Of Finite Groups written by I. Martin Isaacs and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-21 with Mathematics categories.

Character theory is a powerful tool for understanding finite groups. In particular, the theory has been a key ingredient in the classification of finite simple groups. Characters are also of interest in their own right, and their properties are closely related to properties of the structure of the underlying group. The book begins by developing the module theory of complex group algebras. After the module-theoretic foundations are laid in the first chapter, the focus is primarily on characters. This enhances the accessibility of the material for students, which was a major consideration in the writing. Also with students in mind, a large number of problems are included, many of them quite challenging. In addition to the development of the basic theory (using a cleaner notation than previously), a number of more specialized topics are covered with accessible presentations. These include projective representations, the basics of the Schur index, irreducible character degrees and group structure, complex linear groups, exceptional characters, and a fairly extensive introduction to blocks and Brauer characters. This is a corrected reprint of the original 1976 version, later reprinted by Dover. Since 1976 it has become the standard reference for character theory, appearing in the bibliography of almost every research paper in the subject. It is largely self-contained, requiring of the reader only the most basic facts of linear algebra, group theory, Galois theory and ring and module theory.

The Character Theory Of Finite Groups Of Lie Type

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Author : Meinolf Geck
language : en
Publisher: Cambridge University Press
Release Date : 2020-02-27

The Character Theory Of Finite Groups Of Lie Type written by Meinolf Geck and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-27 with Mathematics categories.

Through the fundamental work of Deligne and Lusztig in the 1970s, further developed mainly by Lusztig, the character theory of reductive groups over finite fields has grown into a rich and vast area of mathematics. It incorporates tools and methods from algebraic geometry, topology, combinatorics and computer algebra, and has since evolved substantially. With this book, the authors meet the need for a contemporary treatment, complementing in core areas the well-established books of Carter and Digne–Michel. Focusing on applications in finite group theory, the authors gather previously scattered results and allow the reader to get to grips with the large body of literature available on the subject, covering topics such as regular embeddings, the Jordan decomposition of characters, d-Harish–Chandra theory and Lusztig induction for unipotent characters. Requiring only a modest background in algebraic geometry, this useful reference is suitable for beginning graduate students as well as researchers.

Representations And Characters Of Finite Groups

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Author : M. J. Collins
language : en
Publisher: Cambridge University Press
Release Date : 1990-03-22

Representations And Characters Of Finite Groups written by M. J. Collins and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-03-22 with Mathematics categories.

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.

Characters And Blocks Of Finite Groups

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Author : Gabriel Navarro
language : en
Publisher: Cambridge University Press
Release Date : 1998-05-07

Characters And Blocks Of Finite Groups written by Gabriel Navarro and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-05-07 with Mathematics categories.

This is a clear, accessible and up-to-date exposition of modular representation theory of finite groups from a character-theoretic viewpoint. After a short review of the necessary background material, the early chapters introduce Brauer characters and blocks and develop their basic properties. The next three chapters study and prove Brauer's first, second and third main theorems in turn. These results are then applied to prove a major application of finite groups, the Glauberman Z*-theorem. Later chapters examine Brauer characters in more detail. The relationship between blocks and normal subgroups is also explored and the modular characters and blocks in p-solvable groups are discussed. Finally, the character theory of groups with a Sylow p-subgroup of order p is studied. Each chapter concludes with a set of problems. The book is aimed at graduate students, with some previous knowledge of ordinary character theory, and researchers studying the representation theory of finite groups.

Representations And Characters Of Groups

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Author : Gordon James
language : en
Publisher: Cambridge University Press
Release Date : 2001-10-18

Representations And Characters Of Groups written by Gordon James and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-10-18 with Mathematics categories.

This book provides a modern introduction to the representation theory of finite groups. Now in its second edition, the authors have revised the text and added much new material. The theory is developed in terms of modules, since this is appropriate for more advanced work, but considerable emphasis is placed upon constructing characters. Included here are the character tables of all groups of order less than 32, and all simple groups of order less than 1000. Applications covered include Burnside's paqb theorem, the use of character theory in studying subgroup structure and permutation groups, and how to use representation theory to investigate molecular vibration. Each chapter features a variety of exercises, with full solutions provided at the end of the book. This will be ideal as a course text in representation theory, and in view of the applications, will be of interest to chemists and physicists as well as mathematicians.

Character Theory Of Finite Groups

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Author : Bertram Huppert
language : en
Publisher: Walter de Gruyter
Release Date : 2011-04-20

Character Theory Of Finite Groups written by Bertram Huppert and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04-20 with Mathematics categories.

No detailed description available for "Character Theory of Finite Groups".

Characters Of Finite Groups

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Author : Walter Feit
language : en
Publisher:
Release Date : 1965

Characters Of Finite Groups written by Walter Feit and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Characters of groups categories.

Representation Theory Of Finite Groups

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Author : Benjamin Steinberg
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-10-23

Representation Theory Of Finite Groups written by Benjamin Steinberg and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-23 with Mathematics categories.

This book is intended to present group representation theory at a level accessible to mature undergraduate students and beginning graduate students. This is achieved by mainly keeping the required background to the level of undergraduate linear algebra, group theory and very basic ring theory. Module theory and Wedderburn theory, as well as tensor products, are deliberately avoided. Instead, we take an approach based on discrete Fourier Analysis. Applications to the spectral theory of graphs are given to help the student appreciate the usefulness of the subject. A number of exercises are included. This book is intended for a 3rd/4th undergraduate course or an introductory graduate course on group representation theory. However, it can also be used as a reference for workers in all areas of mathematics and statistics.

Representation Theory Of Finite Groups

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Author : Martin Burrow
language : en
Publisher: Courier Corporation
Release Date : 2014-05-05

Representation Theory Of Finite Groups written by Martin Burrow and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-05 with Mathematics categories.

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

The Theory Of Group Characters And Matrix Representations Of Groups

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Author : Dudley Ernest Littlewood
language : en
Publisher: American Mathematical Soc.
Release Date : 1977

The Theory Of Group Characters And Matrix Representations Of Groups written by Dudley Ernest Littlewood and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977 with Mathematics categories.

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.