Permutation Representations Of Finite Group

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A Course in Finite Group Representation Theory

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Author : Peter Webb
Publisher : Cambridge University Press
ISBN 13 : 1107162394
Total Pages : 339 pages
Book Rating : 4.1/5 (71 download)

Book Synopsis A Course in Finite Group Representation Theory by : Peter Webb

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.

Finite Permutation Groups

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Author : Helmut Wielandt
Publisher : Academic Press
ISBN 13 : 1483258297
Total Pages : 125 pages
Book Rating : 4.4/5 (832 download)

Book Synopsis Finite Permutation Groups by : Helmut Wielandt

Download or read book Finite Permutation Groups written by Helmut Wielandt and published by Academic Press. This book was released on 2014-05-10 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite Permutation Groups provides an introduction to the basic facts of both the theory of abstract finite groups and the theory of permutation groups. This book deals with older theorems on multiply transitive groups as well as on simply transitive groups. Organized into five chapters, this book begins with an overview of the fundamental concepts of notation and Frobenius group. This text then discusses the modifications of multiple transitivity and can be used to deduce an improved form of the classical theorem. Other chapters consider the concept of simply transitive permutation groups. This book discusses as well permutation groups in the framework of representation theory. The final chapter deals with Frobenius' theory of group characters. This book is a valuable resource for engineers, mathematicians, and research workers. Graduate students and readers who are interested in finite permutation groups will also find this book useful.

Representation Theory of Finite Groups

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Author : Benjamin Steinberg
Publisher : Springer Science & Business Media
ISBN 13 : 1461407761
Total Pages : 166 pages
Book Rating : 4.4/5 (614 download)

Book Synopsis Representation Theory of Finite Groups by : Benjamin Steinberg

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.

Permutation Groups

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Author : John D. Dixon
Publisher : Springer Science & Business Media
ISBN 13 : 1461207312
Total Pages : 360 pages
Book Rating : 4.4/5 (612 download)

Book Synopsis Permutation Groups by : John D. Dixon

Download or read book Permutation Groups written by John D. Dixon and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Following the basic ideas, standard constructions and important examples in the theory of permutation groups, the book goes on to develop the combinatorial and group theoretic structure of primitive groups leading to the proof of the pivotal ONan-Scott Theorem which links finite primitive groups with finite simple groups. Special topics covered include the Mathieu groups, multiply transitive groups, and recent work on the subgroups of the infinite symmetric groups. With its many exercises and detailed references to the current literature, this text can serve as an introduction to permutation groups in a course at the graduate or advanced undergraduate level, as well as for self-study.

Local Representation Theory

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Author : J. L. Alperin
Publisher : Cambridge University Press
ISBN 13 : 9780521449267
Total Pages : 198 pages
Book Rating : 4.4/5 (492 download)

Book Synopsis Local Representation Theory by : J. L. Alperin

Download or read book Local Representation Theory written by J. L. Alperin and published by Cambridge University Press. This book was released on 1993-09-24 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this text is to present some of the key results in the representation theory of finite groups. In order to keep the account reasonably elementary, so that it can be used for graduate-level courses, Professor Alperin has concentrated on local representation theory, emphasising module theory throughout. In this way many deep results can be obtained rather quickly. After two introductory chapters, the basic results of Green are proved, which in turn lead in due course to Brauer's First Main Theorem. A proof of the module form of Brauer's Second Main Theorem is then presented, followed by a discussion of Feit's work connecting maps and the Green correspondence. The work concludes with a treatment, new in part, of the Brauer-Dade theory. As a text, this book contains ample material for a one semester course. Exercises are provided at the end of most sections; the results of some are used later in the text. Representation theory is applied in number theory, combinatorics and in many areas of algebra. This book will serve as an excellent introduction to those interested in the subject itself or its applications.

Representation Theory of Finite Groups

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Author : Martin Burrow
Publisher : Academic Press
ISBN 13 : 1483258211
Total Pages : 196 pages
Book Rating : 4.4/5 (832 download)

Book Synopsis Representation Theory of Finite Groups by : Martin Burrow

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.

Projective Representations of Finite Groups

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Author : Gregory Karpilovsky
Publisher :
ISBN 13 :
Total Pages : 672 pages
Book Rating : 4.3/5 (91 download)

Book Synopsis Projective Representations of Finite Groups by : Gregory Karpilovsky

Download or read book Projective Representations of Finite Groups written by Gregory Karpilovsky and published by . This book was released on 1985 with total page 672 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a systematic account of this topic, from the classical foundations established by Schur 80 years ago to current advances and developments in the field. This work focuses on general methods and builds theory solidly on the study of modules over twisted group algebras, and provides a wide range of skill-sharpening mathematical techniques applicable to this subject. Offers an understanding of projective representations of finite groups for algebraists, number theorists, mathematical researchers studying modern algebra, and theoretical physicists.

Representations of Finite and Compact Groups

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Author : Barry Simon
Publisher : American Mathematical Soc.
ISBN 13 : 0821804537
Total Pages : 280 pages
Book Rating : 4.8/5 (218 download)

Book Synopsis Representations of Finite and Compact Groups by : Barry Simon

Download or read book Representations of Finite and Compact Groups written by Barry Simon and published by American Mathematical Soc.. This book was released on 1996 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is a comprehensive pedagogical presentation of the theory of representation of finite and compact Lie groups. It considers both the general theory and representation of specific groups. Representation theory is discussed on the following types of groups: finite groups of rotations, permutation groups, and classical compact semisimple Lie groups. Along the way, the structure theory of the compact semisimple Lie groups is exposed. This is aimed at research mathematicians and graduate students studying group theory.

Quipu: Decorated Permutation Representations Of Finite Groups

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Author : Yongju Bae
Publisher : World Scientific
ISBN 13 : 9811292779
Total Pages : 456 pages
Book Rating : 4.8/5 (112 download)

Book Synopsis Quipu: Decorated Permutation Representations Of Finite Groups by : Yongju Bae

Download or read book Quipu: Decorated Permutation Representations Of Finite Groups written by Yongju Bae and published by World Scientific. This book was released on 2024-06-27 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies dihedral groups, dicyclic groups, other finite subgroups of the 3-dimensional sphere, and the 2-fold extensions of the symmetric group on 4 letters from the point of view of decorated string diagrams of permutations. These are our metaphorical quipu. As you might expect, the book is replete with illustrations. In (almost) all cases, explicit diagrams for the elements of the group are given. The exception is the binary icosahedral group in which only the generators and relations are exhibited.

Graphs on Surfaces and Their Applications

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Author : Sergei K. Lando
Publisher : Springer Science & Business Media
ISBN 13 : 3540383611
Total Pages : 463 pages
Book Rating : 4.5/5 (43 download)

Book Synopsis Graphs on Surfaces and Their Applications by : Sergei K. Lando

Download or read book Graphs on Surfaces and Their Applications written by Sergei K. Lando and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graphs drawn on two-dimensional surfaces have always attracted researchers by their beauty and by the variety of difficult questions to which they give rise. The theory of such embedded graphs, which long seemed rather isolated, has witnessed the appearance of entirely unexpected new applications in recent decades, ranging from Galois theory to quantum gravity models, and has become a kind of a focus of a vast field of research. The book provides an accessible introduction to this new domain, including such topics as coverings of Riemann surfaces, the Galois group action on embedded graphs (Grothendieck's theory of "dessins d'enfants"), the matrix integral method, moduli spaces of curves, the topology of meromorphic functions, and combinatorial aspects of Vassiliev's knot invariants and, in an appendix by Don Zagier, the use of finite group representation theory. The presentation is concrete throughout, with numerous figures, examples (including computer calculations) and exercises, and should appeal to both graduate students and researchers.

Representing Finite Groups

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Author : Ambar N. Sengupta
Publisher : Springer Science & Business Media
ISBN 13 : 1461412315
Total Pages : 383 pages
Book Rating : 4.4/5 (614 download)

Book Synopsis Representing Finite Groups by : Ambar N. Sengupta

Download or read book Representing Finite Groups written by Ambar N. Sengupta and published by Springer Science & Business Media. This book was released on 2011-12-09 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.

Finite Group Theory

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Author : M. Aschbacher
Publisher : Cambridge University Press
ISBN 13 : 9780521786751
Total Pages : 320 pages
Book Rating : 4.7/5 (867 download)

Book Synopsis Finite Group Theory by : M. Aschbacher

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: During the last 40 years the theory of finite groups has developed dramatically. The finite simple groups have been classified and are becoming better understood. Tools exist to reduce many questions about arbitrary finite groups to similar questions about simple groups. Since the classification there have been numerous applications of this theory in other branches of mathematics. Finite Group Theory develops the foundations of the theory of finite groups. It can serve as a text for a course on finite groups for students already exposed to a first course in algebra. It could supply the background necessary to begin reading journal articles in the field. For specialists it also provides a reference on the foundations of the subject. This second edition has been considerably improved with a completely rewritten Chapter 15 considering the 2-Signalizer Functor Theorem, and the addition of an appendix containing solutions to exercises.

Applications of Finite Groups

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Author : J. S. Lomont
Publisher : Academic Press
ISBN 13 : 1483268969
Total Pages : 359 pages
Book Rating : 4.4/5 (832 download)

Book Synopsis Applications of Finite Groups by : J. S. Lomont

Download or read book Applications of Finite Groups written by J. S. Lomont and published by Academic Press. This book was released on 2014-05-12 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: Applications of Finite Groups focuses on the applications of finite groups to problems of physics, including representation theory, crystals, wave equations, and nuclear and molecular structures. The book first elaborates on matrices, groups, and representations. Topics include abstract properties, applications, matrix groups, key theorem of representation theory, properties of character tables, simply reducible groups, tensors and invariants, and representations generated by functions. The text then examines applications and subgroups and representations, as well as subduced and induced representations, fermion annihilation and creation operators, crystallographic point groups, proportionality tensors in crystals, and nonrelativistic wave equations. The publication takes a look at space group representations and energy bands, symmetric groups, and applications. Topics include molecular and nuclear structures, multiplet splitting in crystalline electric fields, construction of irreducible representations of the symmetric groups, and reality of representations. The manuscript is a dependable source of data for physicists and researchers interested in the applications of finite groups.

Representations and Characters of Groups

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Author : Gordon James
Publisher : Cambridge University Press
ISBN 13 : 1139811053
Total Pages : 436 pages
Book Rating : 4.1/5 (398 download)

Book Synopsis Representations and Characters of Groups by : Gordon James

Download or read book Representations and Characters of Groups written by Gordon James and published by Cambridge University Press. This book was released on 2001-10-18 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Representations of Finite Classical Groups

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Author : A. V. Zelevinsky
Publisher : Springer
ISBN 13 : 3540387110
Total Pages : 189 pages
Book Rating : 4.5/5 (43 download)

Book Synopsis Representations of Finite Classical Groups by : A. V. Zelevinsky

Download or read book Representations of Finite Classical Groups written by A. V. Zelevinsky and published by Springer. This book was released on 2006-11-14 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Representations of the Infinite Symmetric Group

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Author : Alexei Borodin
Publisher : Cambridge University Press
ISBN 13 : 1107175550
Total Pages : 169 pages
Book Rating : 4.1/5 (71 download)

Book Synopsis Representations of the Infinite Symmetric Group by : Alexei Borodin

Download or read book Representations of the Infinite Symmetric Group written by Alexei Borodin and published by Cambridge University Press. This book was released on 2017 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the modern representation theory of big groups, exploring its connections to probability and algebraic combinatorics.

Group Representations in Probability and Statistics

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Author : Persi Diaconis
Publisher : Ims
ISBN 13 :
Total Pages : 212 pages
Book Rating : 4.3/5 (91 download)

Book Synopsis Group Representations in Probability and Statistics by : Persi Diaconis

Download or read book Group Representations in Probability and Statistics written by Persi Diaconis and published by Ims. This book was released on 1988 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: