A Course on Finite Groups

Author: H.E. Rose

Publisher: Springer Science & Business Media

ISBN: 9781848828896

Category: Mathematics

Page: 311

View: 9538

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.

Finite Groups

A Second Course on Group Theory

Author: Bertram A. F. Wehrfritz

Publisher: World Scientific

ISBN: 9789810238742

Category: Mathematics

Page: 123

View: 5947

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.

The Form of Finite Groups

A Course on Finite Group Theory

Author: Stephen G Odaibo M D

Publisher: Symmetry Seed Books

ISBN: 9780997116304


Page: 242

View: 3358

Group theory is the language in which our natural world is expressed. Everything from Einstein's theory of relativity to the inner workings of electrons, protons, and quarks are encoded in the language of group theory. This book on finite group theory is a great resource for both undergraduate and graduate students in the Mathematical sciences. It will also be found indispensable by anyone serious about acquiring a fundamental understanding of our physical world.

A Course on Group Theory

Author: John S. Rose

Publisher: Courier Corporation

ISBN: 0486170667

Category: Mathematics

Page: 320

View: 5213

Text for advanced courses in group theory focuses on finite groups, with emphasis on group actions. Explores normal and arithmetical structures of groups as well as applications. 679 exercises. 1978 edition.

A Course in Finite Group Representation Theory

Author: Peter Webb

Publisher: Cambridge University Press

ISBN: 1107162394

Category: Mathematics

Page: 328

View: 8337

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.

Structure Theory for Canonical Classes of Finite Groups

Author: Wenbin Guo

Publisher: Springer

ISBN: 3662457474

Category: Mathematics

Page: 359

View: 9131

This book offers a systematic introduction to recent achievements and development in research on the structure of finite non-simple groups, the theory of classes of groups and their applications. In particular, the related systematic theories are considered and some new approaches and research methods are described – e.g., the F-hypercenter of groups, X-permutable subgroups, subgroup functors, generalized supplementary subgroups, quasi-F-group, and F-cohypercenter for Fitting classes. At the end of each chapter, we provide relevant supplementary information and introduce readers to selected open problems.

Classes of Finite Groups

Author: Adolfo Ballester-Bolinches,Luis M. Ezquerro

Publisher: Springer Science & Business Media

ISBN: 1402047193

Category: Mathematics

Page: 381

View: 4074

This book covers the latest achievements of the Theory of Classes of Finite Groups. It introduces some unpublished and fundamental advances in this Theory and provides a new insight into some classic facts in this area. By gathering the research of many authors scattered in hundreds of papers the book contributes to the understanding of the structure of finite groups by adapting and extending the successful techniques of the Theory of Finite Soluble Groups.

Finite Group Theory

Author: M. Aschbacher

Publisher: Cambridge University Press

ISBN: 9780521786751

Category: Mathematics

Page: 304

View: 1278

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.

Endliche Gruppen

Eine Einführung in die Theorie der endlichen Gruppen

Author: H. Kurzweil

Publisher: Springer-Verlag

ISBN: 3642953131

Category: Mathematics

Page: 190

View: 8426

A Course in the Theory of Groups

Author: Derek J.S. Robinson

Publisher: Springer Science & Business Media

ISBN: 1441985948

Category: Mathematics

Page: 502

View: 409

"An excellent up-to-date introduction to the theory of groups. It is general yet comprehensive, covering various branches of group theory. The 15 chapters contain the following main topics: free groups and presentations, free products, decompositions, Abelian groups, finite permutation groups, representations of groups, finite and infinite soluble groups, group extensions, generalizations of nilpotent and soluble groups, finiteness properties." —-ACTA SCIENTIARUM MATHEMATICARUM

A Course in Group Theory

Author: J. F. Humphreys

Publisher: Oxford University Press on Demand

ISBN: 9780198534594

Category: Business & Economics

Page: 279

View: 5564

Each chapter ends with a summary of the material covered and notes on the history and development of group theory.

Sylow Theory, Formations, and Fitting Classes in Locally Finite Groups

Author: Martyn Russell Dixon

Publisher: World Scientific

ISBN: 9789810217952

Category: Mathematics

Page: 304

View: 8564

This book is concerned with the generalizations of Sylow theorems and the related topics of formations and the fitting of classes to locally finite groups. It also contains details of Sunkov's and Belyaev'ss results on locally finite groups with min-p for all primes p. This is the first time many of these topics have appeared in book form. The body of work here is fairly complete.

Harmonic Analysis on Finite Groups

Representation Theory, Gelfand Pairs and Markov Chains

Author: Tullio Ceccherini-Silberstein,Fabio Scarabotti,Filippo Tolli

Publisher: Cambridge University Press

ISBN: 1139470809

Category: Mathematics

Page: N.A

View: 2687

Line up a deck of 52 cards on a table. Randomly choose two cards and switch them. How many switches are needed in order to mix up the deck? Starting from a few concrete problems such as random walks on the discrete circle and the finite ultrametric space this book develops the necessary tools for the asymptotic analysis of these processes. This detailed study culminates with the case-by-case analysis of the cut-off phenomenon discovered by Persi Diaconis. This self-contained text is ideal for graduate students and researchers working in the areas of representation theory, group theory, harmonic analysis and Markov chains. Its topics range from the basic theory needed for students new to this area, to advanced topics such as the theory of Green's algebras, the complete analysis of the random matchings, and the representation theory of the symmetric group.

Linear Representations of Finite Groups

Author: Jean-Pierre Serre

Publisher: Springer Science & Business Media

ISBN: 1468494589

Category: Mathematics

Page: 172

View: 2144

This book consists of three parts, rather different in level and purpose. The first part was originally written for quantum chemists. It describes the correspondence, due to Frobenius, between linear representations and characters. The second part is a course given in 1966 to second-year students of l’Ecole Normale. It completes in a certain sense the first part. The third part is an introduction to Brauer Theory.

Representation Theory of Finite Groups

Author: Martin Burrow

Publisher: Courier Corporation

ISBN: 0486145077

Category: Mathematics

Page: 208

View: 9320

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

A Course in Number Theory and Cryptography

Author: Neal Koblitz

Publisher: Springer Science & Business Media

ISBN: 9780387942933

Category: Mathematics

Page: 235

View: 3976

This is a substantially revised and updated introduction to arithmetic topics, both ancient and modern, that have been at the centre of interest in applications of number theory, particularly in cryptography. As such, no background in algebra or number theory is assumed, and the book begins with a discussion of the basic number theory that is needed. The approach taken is algorithmic, emphasising estimates of the efficiency of the techniques that arise from the theory, and one special feature is the inclusion of recent applications of the theory of elliptic curves. Extensive exercises and careful answers are an integral part all of the chapters.

Finite Groups of Automorphisms

Course Given at the University of Southampton, October-December 1969

Author: Norman Biggs

Publisher: CUP Archive

ISBN: 9780521082150

Category: Finite groups

Page: 117

View: 9046

Cohomology Rings of Finite Groups

With an Appendix: Calculations of Cohomology Rings of Groups of Order Dividing 64

Author: Jon F. Carlson,L. Townsley,Luís Valero-Elizondo,Mucheng Zhang

Publisher: Springer Science & Business Media

ISBN: 9401702152

Category: Mathematics

Page: 776

View: 7125

Group cohomology has a rich history that goes back a century or more. Its origins are rooted in investigations of group theory and num ber theory, and it grew into an integral component of algebraic topology. In the last thirty years, group cohomology has developed a powerful con nection with finite group representations. Unlike the early applications which were primarily concerned with cohomology in low degrees, the in teractions with representation theory involve cohomology rings and the geometry of spectra over these rings. It is this connection to represen tation theory that we take as our primary motivation for this book. The book consists of two separate pieces. Chronologically, the first part was the computer calculations of the mod-2 cohomology rings of the groups whose orders divide 64. The ideas and the programs for the calculations were developed over the last 10 years. Several new features were added over the course of that time. We had originally planned to include only a brief introduction to the calculations. However, we were persuaded to produce a more substantial text that would include in greater detail the concepts that are the subject of the calculations and are the source of some of the motivating conjectures for the com putations. We have gathered together many of the results and ideas that are the focus of the calculations from throughout the mathematical literature.