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Author : Louis Clark Mathewson
Publisher :
ISBN 13 :
Total Pages : 188 pages
Book Rating : 4.3/5 (91 download)
Download or read book Elementary Theory of Finite Groups written by Louis Clark Mathewson and published by . This book was released on 1930 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : I. Martin Isaacs
Publisher : American Mathematical Soc.
ISBN 13 : 0821842293
Total Pages : 322 pages
Book Rating : 4.8/5 (218 download)
Download or read book Character Theory of Finite Groups written by I. Martin Isaacs and published by American Mathematical Soc.. This book was released on 2006-11-21 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Benjamin Steinberg
Publisher : Springer Science & Business Media
ISBN 13 : 1461407761
Total Pages : 166 pages
Book Rating : 4.4/5 (614 download)
Download or read book Representation Theory of Finite Groups written by Benjamin Steinberg and published by Springer Science & Business Media. This book was released on 2011-10-23 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Martin Burrow
Publisher : Academic Press
ISBN 13 : 1483258211
Total Pages : 196 pages
Book Rating : 4.4/5 (832 download)
Download or read book Representation Theory of Finite Groups written by Martin Burrow and published by Academic Press. This book was released on 2014-05-10 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Pavel I. Etingof
Publisher : American Mathematical Soc.
ISBN 13 : 0821853511
Total Pages : 240 pages
Book Rating : 4.8/5 (218 download)
Download or read book Introduction to Representation Theory written by Pavel I. Etingof and published by American Mathematical Soc.. This book was released on 2011 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory. The goal of this book is to give a ``holistic'' introduction to representation theory, presenting it as a unified subject which studies representations of associative algebras and treating the representation theories of groups, Lie algebras, and quivers as special cases. Using this approach, the book covers a number of standard topics in the representation theories of these structures. Theoretical material in the book is supplemented by many problems and exercises which touch upon a lot of additional topics; the more difficult exercises are provided with hints. The book is designed as a textbook for advanced undergraduate and beginning graduate students. It should be accessible to students with a strong background in linear algebra and a basic knowledge of abstract algebra.
Author : B. Huppert
Publisher : Springer Science & Business Media
ISBN 13 : 3642679943
Total Pages : 545 pages
Book Rating : 4.6/5 (426 download)
Download or read book Finite Groups II written by B. Huppert and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: 17):~t? L It CIFDr- ! wei! unsre Weisheit Einfalt ist, From "Lohengrin", Richard Wagner At the time of the appearance of the first volume of this work in 1967, the tempestuous development of finite group theory had already made it virtually impossible to give a complete presentation of the subject in one treatise. The present volume and its successor have therefore the more modest aim of giving descriptions of the recent development of certain important parts of the subject, and even in these parts no attempt at completeness has been made. Chapter VII deals with the representation theory of finite groups in arbitrary fields with particular attention to those of non-zero charac teristic. That part of modular representation theory which is essentially the block theory of complex characters has not been included, as there are already monographs on this subject and others will shortly appear. Instead, we have restricted ourselves to such results as can be obtained by purely module-theoretical means.
Author : Peter Webb
Publisher : Cambridge University Press
ISBN 13 : 1107162394
Total Pages : 339 pages
Book Rating : 4.1/5 (71 download)
Download or read book A Course in Finite Group Representation Theory written by Peter Webb and published by Cambridge University Press. This book was released on 2016-08-19 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Hans Kurzweil
Publisher : Springer Science & Business Media
ISBN 13 : 0387217681
Total Pages : 390 pages
Book Rating : 4.3/5 (872 download)
Download or read book The Theory of Finite Groups written by Hans Kurzweil and published by Springer Science & Business Media. This book was released on 2006-03-04 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: From reviews of the German edition: "This is an exciting text and a refreshing contribution to an area in which challenges continue to flourish and to captivate the viewer. Even though representation theory and constructions of simple groups have been omitted, the text serves as a springboard for deeper study in many directions." Mathematical Reviews
Author : H.E. Rose
Publisher : Springer Science & Business Media
ISBN 13 : 1848828896
Total Pages : 314 pages
Book Rating : 4.8/5 (488 download)
Download or read book A Course on Finite Groups written by H.E. Rose and published by Springer Science & Business Media. This book was released on 2009-12-16 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduces the richness of group theory to advanced undergraduate and graduate students, concentrating on the finite aspects. Provides a wealth of exercises and problems to support self-study. Additional online resources on more challenging and more specialised topics can be used as extension material for courses, or for further independent study.
Author : I. Martin Isaacs
Publisher : American Mathematical Soc.
ISBN 13 : 9780821884096
Total Pages : 376 pages
Book Rating : 4.8/5 (84 download)
Download or read book Finite Group Theory written by I. Martin Isaacs and published by American Mathematical Soc.. This book was released on 2008-01-01 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: The text begins with a review of group actions and Sylow theory. It includes semidirect products, the Schur-Zassenhaus theorem, the theory of commutators, coprime actions on groups, transfer theory, Frobenius groups, primitive and multiply transitive permutation groups, the simplicity of the PSL groups, the generalized Fitting subgroup and also Thompson's J-subgroup and his normal $p$-complement theorem.
Author : Ambar N. Sengupta
Publisher : Springer Science & Business Media
ISBN 13 : 1461412307
Total Pages : 383 pages
Book Rating : 4.4/5 (614 download)
Download or read book Representing Finite Groups written by Ambar N. Sengupta and published by Springer Science & Business Media. This book was released on 2011-12-08 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate textbook presents the basics of representation theory for finite groups from the point of view of semisimple algebras and modules over them. The presentation interweaves insights from specific examples with development of general and powerful tools based on the notion of semisimplicity. The elegant ideas of commutant duality are introduced, along with an introduction to representations of unitary groups. The text progresses systematically and the presentation is friendly and inviting. Central concepts are revisited and explored from multiple viewpoints. Exercises at the end of the chapter help reinforce the material. Representing Finite Groups: A Semisimple Introduction would serve as a textbook for graduate and some advanced undergraduate courses in mathematics. Prerequisites include acquaintance with elementary group theory and some familiarity with rings and modules. A final chapter presents a self-contained account of notions and results in algebra that are used. Researchers in mathematics and mathematical physics will also find this book useful. A separate solutions manual is available for instructors.
Author : Mark L. Lewis
Publisher : American Mathematical Soc.
ISBN 13 : 0821848275
Total Pages : 194 pages
Book Rating : 4.8/5 (218 download)
Download or read book Character Theory of Finite Groups written by Mark L. Lewis and published by American Mathematical Soc.. This book was released on 2010-09-17 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Charles W. Curtis
Publisher : American Mathematical Soc.
ISBN 13 : 0821840665
Total Pages : 714 pages
Book Rating : 4.8/5 (218 download)
Download or read book Representation Theory of Finite Groups and Associative Algebras written by Charles W. Curtis and published by American Mathematical Soc.. This book was released on 2006 with total page 714 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides an introduction to various aspects of the representation theory of finite groups. This book covers such topics as general non-commutative algebras, Frobenius algebras, representations over non-algebraically closed fields and fields of non-zero characteristic, and integral representations.
Author : Gerhard Michler
Publisher : Cambridge University Press
ISBN 13 : 0521866251
Total Pages : 638 pages
Book Rating : 4.5/5 (218 download)
Download or read book Theory of Finite Simple Groups written by Gerhard Michler and published by Cambridge University Press. This book was released on 2006-09-21 with total page 638 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first representation theoretic and algorithmic approach to the theory of abstract finite simple groups.
Author : Bertram A. F. Wehrfritz
Publisher : World Scientific
ISBN 13 : 9789810238742
Total Pages : 138 pages
Book Rating : 4.2/5 (387 download)
Download or read book Finite Groups written by Bertram A. F. Wehrfritz and published by World Scientific. This book was released on 1999 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of groups, especially of finite groups, is one of the most delightful areas of mathematics. Its proofs often have elegance and crystalline beauty. This textbook is intended for the reader who has been exposed to about three years of serious mathematics. The notion of a group appears widely in mathematics and even further afield in physics and chemistry, and the fundamental idea should be known to all mathematicians. In this textbook a purely algebraic approach is taken and the choice of material is based upon the notion of conjugacy. The aim is not only to cover basic material, but also to present group theory as a living, vibrant and growing discipline, by including references and discussion of some work up to the present day.
Author : M. Aschbacher
Publisher : Cambridge University Press
ISBN 13 : 9780521786751
Total Pages : 320 pages
Book Rating : 4.7/5 (867 download)
Download or read book Finite Group Theory written by M. Aschbacher and published by Cambridge University Press. This book was released on 2000-06-26 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides the basic foundations for the local theory of finite groups, the theory of classical linear groups, and the theory of buildings and BN-pairs.
Author : Hirosi Nagao
Publisher : Elsevier
ISBN 13 : 1483269930
Total Pages : 443 pages
Book Rating : 4.4/5 (832 download)
Download or read book Representations of Finite Groups written by Hirosi Nagao and published by Elsevier. This book was released on 2014-05-10 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: Representations of Finite Groups provides an account of the fundamentals of ordinary and modular representations. This book discusses the fundamental theory of complex representations of finite groups. Organized into five chapters, this book begins with an overview of the basic facts about rings and modules. This text then provides the theory of algebras, including theories of simple algebras, Frobenius algebras, crossed products, and Schur indices with representation-theoretic versions of them. Other chapters include a survey of the fundamental theory of modular representations, with emphasis on Brauer characters. This book discusses as well the module-theoretic representation theory due to Green and includes some topics such as Burry–Carlson's theorem and Scott modules. The final chapter deals with the fundamental results of Brauer on blocks and Fong's theory of covering, and includes some approaches to them. This book is a valuable resource for readers who are interested in the various approaches to the study of the representations of groups.
