Characters Of Finite Groups Part 1

Author : IA. G. Berkovich E. M. Zhmud'
Publisher : American Mathematical Soc.
Page : 414 pages
File Size : 47,5 Mb
Release : 1997-12-02
Category : Electronic
ISBN : 0821897829

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Characters of Finite Groups. Part 1 by IA. G. Berkovich E. M. Zhmud' Pdf

This book discusses character theory and its applications to finite groups. The work places the subject within the reach of people with a relatively modest mathematical background. The necessary background exceeds the standard algebra course with respect only to finite groups. Starting with basic notions and theorems in character theory, the authors present a variety of results on the properties of complex-valued characters and applications to finite groups. The main themes are degrees and kernels of irreducible characters, the class number and the number of nonlinear irreducible characters, values of irreducible characters, characterizations and generalizations of Frobenius groups, and generalizations and applications of monomial groups. The presentation is detailed, and many proofs of known results are new. Most of the results in the book are presented in monograph form for the first time. Numerous exercises offer additional information on the topics and help readers to understand the main concepts and results.

Author : Yakov G. Berkovich,Lev S. Kazarin,Emmanuel M. Zhmud'
Publisher : Walter de Gruyter GmbH & Co KG
Page : 623 pages
File Size : 40,5 Mb
Release : 2017-12-18
Category : Mathematics
ISBN : 9783110224078

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Volume 1 by Yakov G. Berkovich,Lev S. Kazarin,Emmanuel M. Zhmud' Pdf

This updated edition of this classic book is devoted to ordinary representation theory and is addressed to finite group theorists intending to study and apply character theory. It contains many exercises and examples, and the list of problems contains a number of open questions.

Author : I. Martin Isaacs
Publisher : American Mathematical Soc.
Page : 322 pages
File Size : 41,6 Mb
Release : 2006-11-21
Category : Mathematics
ISBN : 9780821842294

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Character Theory of Finite Groups by I. Martin Isaacs Pdf

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.

Author : Mark L. Lewis
Publisher : American Mathematical Soc.
Page : 194 pages
File Size : 42,7 Mb
Release : 2010-09-17
Category : Mathematics
ISBN : 9780821848272

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Character Theory of Finite Groups by Mark L. Lewis Pdf

This volume contains a collection of papers from the Conference on Character Theory of Finite Groups, held at the Universitat de Valencia, Spain, on June 3-5, 2009, in honor of I. Martin Isaacs. The topics include permutation groups, character theory, p-groups, and group rings. The research articles feature new results on large normal abelian subgroups of p-groups, construction of certain wreath products, computing idempotents in group algebras of finite groups, and using dual pairs to study representations of cross characteristic in classical groups. The expository articles present results on vertex subgroups, measuring theorems in permutation groups, the development of super character theory, and open problems in character theory.

Author : M. J. Collins
Publisher : Cambridge University Press
Page : 260 pages
File Size : 48,9 Mb
Release : 1990-03-22
Category : Mathematics
ISBN : 0521234409

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Representations and Characters of Finite Groups by M. J. Collins Pdf

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.

Author : Meinolf Geck,Gunter Malle
Publisher : Cambridge University Press
Page : 405 pages
File Size : 48,5 Mb
Release : 2020-02-27
Category : Mathematics
ISBN : 9781108489621

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The Character Theory of Finite Groups of Lie Type by Meinolf Geck,Gunter Malle Pdf

A comprehensive guide to the vast literature and range of results around Lusztig's character theory of finite groups of Lie type.

Author : Bertram Huppert
Publisher : Walter de Gruyter
Page : 625 pages
File Size : 42,9 Mb
Release : 2011-04-20
Category : Mathematics
ISBN : 9783110809237

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Character Theory of Finite Groups by Bertram Huppert Pdf

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

Author : Gabriel Navarro
Publisher : Cambridge University Press
Page : 301 pages
File Size : 46,7 Mb
Release : 1998-05-07
Category : Mathematics
ISBN : 9780521595131

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Characters and Blocks of Finite Groups by Gabriel Navarro Pdf

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.

Author : I︠A︡. G. Berkovich,︠I︡A. G. Berkovich,Ya. G. Berkovich,E. M. Zhmudʹ
Publisher : American Mathematical Soc.
Page : 332 pages
File Size : 43,8 Mb
Release : 1998
Category : Mathematics
ISBN : 0821805320

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Characters of Finite Groups by I︠A︡. G. Berkovich,︠I︡A. G. Berkovich,Ya. G. Berkovich,E. M. Zhmudʹ Pdf

Places character theory and its applications to finite groups. This book focuses on themes such as degrees and kernels of irreducible characters, the class number and the number of nonlinear irreducible characters, values of irreducible characters, characterizations and generalizations of Frobenius groups, and generalizations of monomial groups.

Author : I. Martin Isaacs
Publisher : American Mathematical Soc.
Page : 368 pages
File Size : 45,6 Mb
Release : 2018-05-23
Category : Group theory
ISBN : 9781470434854

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Characters of Solvable Groups by I. Martin Isaacs Pdf

This book, which can be considered as a sequel of the author's famous book Character Theory of Finite Groups, concerns the character theory of finite solvable groups and other groups that have an abundance of normal subgroups. It is subdivided into three parts: -theory, character correspondences, and M-groups. The -theory section contains an exposition of D. Gajendragadkar's -special characters, and it includes various extensions, generalizations, and applications of his work. The character correspondences section proves the McKay character counting conjecture and the Alperin weight conjecture for solvable groups, and it constructs a canonical McKay bijection for odd-order groups. In addition to a review of some basic material on M-groups, the third section contains an exposition of the use of symplectic modules for studying M-groups. In particular, an accessible presentation of E. C. Dade's deep results on monomial characters of odd prime-power degree is included. Very little of this material has previously appeared in book form, and much of it is based on the author's research. By reading a clean and accessible presentation written by the leading expert in the field, researchers and graduate students will be inspired to learn and work in this area that has fascinated the author for decades.

Author : Gordon James,Martin Liebeck
Publisher : Cambridge University Press
Page : 436 pages
File Size : 50,6 Mb
Release : 2001-10-18
Category : Mathematics
ISBN : 9781139811057

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Representations and Characters of Groups by Gordon James,Martin Liebeck Pdf

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.

Author : Peter Webb
Publisher : Cambridge University Press
Page : 339 pages
File Size : 44,9 Mb
Release : 2016-08-19
Category : Mathematics
ISBN : 9781107162396

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A Course in Finite Group Representation Theory by Peter Webb Pdf

This graduate-level text provides a thorough grounding in the representation theory of finite groups over fields and rings. The book provides a balanced and comprehensive account of the subject, detailing the methods needed to analyze representations that arise in many areas of mathematics. Key topics include the construction and use of character tables, the role of induction and restriction, projective and simple modules for group algebras, indecomposable representations, Brauer characters, and block theory. This classroom-tested text provides motivation through a large number of worked examples, with exercises at the end of each chapter that test the reader's knowledge, provide further examples and practice, and include results not proven in the text. Prerequisites include a graduate course in abstract algebra, and familiarity with the properties of groups, rings, field extensions, and linear algebra.

Author : Walter Feit
Publisher : Unknown
Page : 202 pages
File Size : 42,6 Mb
Release : 1967
Category : Characters of groups
ISBN : UOM:39015014354404

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Characters of Finite Groups by Walter Feit Pdf

Author : I_A. G. Berkovich,E. M. Zhmud_
Publisher : American Mathematical Soc.
Page : 364 pages
File Size : 55,7 Mb
Release : 1998-09-29
Category : Mathematics
ISBN : 0821897888

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Characters of Finite Groups by I_A. G. Berkovich,E. M. Zhmud_ Pdf

This book places character theory and its applications to finite groups within the reach of people with a comparatively modest mathematical background. The work concentrates mostly on applications of character theory to finite groups. The main themes are degrees and kernels of irreducible characters, the class number and the number of nonlinear irreducible characters, values of irreducible characters, characterizations and generalizations of Frobenius groups, and generalizations of monomial groups. The presentation is detailed, and many proofs of known results are new.

Author : Paul Fong
Publisher : American Mathematical Soc.
Page : 487 pages
File Size : 49,9 Mb
Release : 1987
Category : Mathematics
ISBN : 9780821814772

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The Arcata Conference on Representations of Finite Groups by Paul Fong Pdf