Character Theory of Finite Groups

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.

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Author: Mark L. Lewis

Publisher: American Mathematical Soc.

ISBN: 9780821848272

Category: Mathematics

Page: 179

View: 723

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.

Character Theory of Finite Groups

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.

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Author: Bertram Huppert

Publisher: Walter de Gruyter

ISBN: 9783110809237

Category: Mathematics

Page: 624

View: 827

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

The Character Theory of Finite Groups of Lie Type

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

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Author: Meinolf Geck

Publisher: Cambridge University Press

ISBN: 9781108489621

Category: Mathematics

Page: 406

View: 126

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

Representations and Characters of Finite 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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Author: M. J. Collins

Publisher: Cambridge University Press

ISBN: 0521234409

Category: Mathematics

Page: 242

View: 648

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 of Finite Groups

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.

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Author: I_A. G. Berkovich

Publisher: American Mathematical Soc.

ISBN: 0821897888

Category: Mathematics

Page: 332

View: 678

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.

Modular Representation Theory of Finite Groups

Some basic algebra together with the semisimple case are assumed to be known, although all facts to be used are restated (without proofs) in the text. Otherwise the book is entirely self-contained.

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Author: Peter Schneider

Publisher: Springer Science & Business Media

ISBN: 9781447148326

Category: Mathematics

Page: 178

View: 463

Representation theory studies maps from groups into the general linear group of a finite-dimensional vector space. For finite groups the theory comes in two distinct flavours. In the 'semisimple case' (for example over the field of complex numbers) one can use character theory to completely understand the representations. This by far is not sufficient when the characteristic of the field divides the order of the group. Modular Representation Theory of finite Groups comprises this second situation. Many additional tools are needed for this case. To mention some, there is the systematic use of Grothendieck groups leading to the Cartan matrix and the decomposition matrix of the group as well as Green's direct analysis of indecomposable representations. There is also the strategy of writing the category of all representations as the direct product of certain subcategories, the so-called 'blocks' of the group. Brauer's work then establishes correspondences between the blocks of the original group and blocks of certain subgroups the philosophy being that one is thereby reduced to a simpler situation. In particular, one can measure how nonsemisimple a category a block is by the size and structure of its so-called 'defect group'. All these concepts are made explicit for the example of the special linear group of two-by-two matrices over a finite prime field. Although the presentation is strongly biased towards the module theoretic point of view an attempt is made to strike a certain balance by also showing the reader the group theoretic approach. In particular, in the case of defect groups a detailed proof of the equivalence of the two approaches is given. This book aims to familiarize students at the masters level with the basic results, tools, and techniques of a beautiful and important algebraic theory. Some basic algebra together with the semisimple case are assumed to be known, although all facts to be used are restated (without proofs) in the text. Otherwise the book is entirely self-contained.

Character Theory of Finite Groups

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.

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Author: I. Martin Isaacs, Mark L. Lewis

Publisher: American Mathematical Soc.

ISBN: 9780821858486

Category: Finite groups

Page: 179

View: 617

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.

The Character Theory of Finite Groups of Lie Type

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.

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Author: Meinolf Geck

Publisher: Cambridge University Press

ISBN: 9781108808903

Category: Mathematics

Page:

View: 665

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.

Representation Theory of Finite Groups

This book is intended to present group representation theory at a level accessible to mature undergraduate students and beginning graduate students.

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Author: Benjamin Steinberg

Publisher: Springer Science & Business Media

ISBN: 1461407761

Category: Mathematics

Page: 157

View: 235

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.

Characters of Finite Groups Part 1

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.

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Author: IA. G. Berkovich E. M. Zhmud'

Publisher: American Mathematical Soc.

ISBN: 0821897829

Category:

Page: 382

View: 686

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.

Character Theory of Finite 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.

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Author: I. Martin Isaacs

Publisher:

ISBN: 1470430355

Category: Characters of groups

Page: 303

View: 849

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.

Representations and Characters of Groups

This book provides a modern introduction to the representation theory of finite groups.

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Author: Gordon James

Publisher: Cambridge University Press

ISBN: 052100392X

Category: Mathematics

Page: 458

View: 433

This book provides a modern introduction to the representation theory of finite groups.

Representation Theory of Finite Groups

The last chapter deals with the construction of irreducible representations of groups. This book will be of great value to graduate students who wish to acquire some knowledge of representation theory.

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Author: Martin Burrow

Publisher: Academic Press

ISBN: 9781483258218

Category: Mathematics

Page: 196

View: 826

Representation Theory of Finite Groups is a five chapter text that covers the standard material of representation theory. This book starts with an overview of the basic concepts of the subject, including group characters, representation modules, and the rectangular representation. The succeeding chapters describe the features of representation theory of rings with identity and finite groups. These topics are followed by a discussion of some of the application of the theory of characters, along with some classical theorems. The last chapter deals with the construction of irreducible representations of groups. This book will be of great value to graduate students who wish to acquire some knowledge of representation theory.

Volume 1

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.

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Author: Yakov G. Berkovich

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 9783110224078

Category: Mathematics

Page: 623

View: 719

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.

Characters of Solvable Groups

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.

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Author: I. Martin Isaacs

Publisher: American Mathematical Soc.

ISBN: 9781470434854

Category: Group theory

Page: 368

View: 761

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.

Groups and Characters

Presuming only a basic knowledge of abstract algebra as in a first-year graduate course, the text opens with a review of background material and then guides readers carefully through several of the most important aspects of groups and ...

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Author: Larry C. Grove

Publisher: John Wiley & Sons

ISBN: 9781118030936

Category: Mathematics

Page: 224

View: 639

An authoritative, full-year course on both group theory and ordinary character theory--essential tools for mathematics and the physical sciences One of the few treatments available combining both group theory and character theory, Groups and Characters is an effective general textbook on these two fundamentally connected subjects. Presuming only a basic knowledge of abstract algebra as in a first-year graduate course, the text opens with a review of background material and then guides readers carefully through several of the most important aspects of groups and characters, concentrating mainly on finite groups. Challenging yet accessible, Groups and Characters features: * An extensive collection of examples surveying many different types of groups, including Sylow subgroups of symmetric groups, affine groups of fields, the Mathieu groups, and symplectic groups * A thorough, easy-to-follow discussion of Polya-Redfield enumeration, with applications to combinatorics * Inclusive explorations of the transfer function and normal complements, induction and restriction of characters, Clifford theory, characters of symmetric and alternating groups, Frobenius groups, and the Schur index * Illuminating accounts of several computational aspects of group theory, such as the Schreier-Sims algorithm, Todd-Coxeter coset enumeration, and algorithms for generating character tables As valuable as Groups and Characters will prove as a textbook for mathematicians, it has broader applications. With chapters suitable for use as independent review units, along with a full bibliography and index, it will be a dependable general reference for chemists, physicists, and crystallographers.

Character Theory of Finite Groups

Character theory provides a powerful tool for proving theorems about finite
groups. In fact, there are some important results, such as Frobenius' theorem, for
which no proof without characters is known. (Until fairly recently, Burnside's p“qb
 ...

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Author: I. Martin Isaacs

Publisher: American Mathematical Soc.

ISBN: 9780821842294

Category: Mathematics

Page: 303

View: 758

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.