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Author: Helmut Wielandt
Publisher: Academic Press
ISBN: 1483258297
Category : Mathematics
Languages : en
Pages : 125
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Book Description
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.
Author: Helmut Wielandt
Publisher: Academic Press
ISBN: 1483258297
Category : Mathematics
Languages : en
Pages : 125
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Book Description
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.
Author: Peter Webb
Publisher: Cambridge University Press
ISBN: 1107162394
Category : Mathematics
Languages : en
Pages : 339
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Book Description
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: Benjamin Steinberg
Publisher: Springer Science & Business Media
ISBN: 1461407761
Category : Mathematics
Languages : en
Pages : 166
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Book Description
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: William S. Burnside
Publisher: Courier Corporation
ISBN: 0486159442
Category : Mathematics
Languages : en
Pages : 545
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Book Description
Classic 1911 edition covers many group-related properties, including an extensive treatment of permutation groups and groups of linear substitutions, along with graphic representation of groups, congruence groups, and special topics.
Author: John Rhodes
Publisher: Springer Science & Business Media
ISBN: 0387097813
Category : Mathematics
Languages : en
Pages : 674
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Book Description
This comprehensive, encyclopedic text in four parts aims to give the reader — from the graduate student to the researcher/practitioner — a detailed understanding of modern finite semigroup theory, focusing in particular on advanced topics on the cutting edge of research. The q-theory of Finite Semigroups presents important techniques and results, many for the first time in book form, thereby updating and modernizing the semigroup theory literature.
Author: Martin W. Liebeck
Publisher: American Mathematical Soc.
ISBN: 082184654X
Category : Mathematics
Languages : en
Pages : 87
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Book Description
Addresses the classical problem of determining finite primitive permutation groups G with a regular subgroup B.
Author: Gena Hahn
Publisher: Springer Science & Business Media
ISBN: 9780792346685
Category : Mathematics
Languages : en
Pages : 456
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Book Description
The last decade has seen two parallel developments, one in computer science, the other in mathematics, both dealing with the same kind of combinatorial structures: networks with strong symmetry properties or, in graph-theoretical language, vertex-transitive graphs, in particular their prototypical examples, Cayley graphs. In the design of large interconnection networks it was realised that many of the most fre quently used models for such networks are Cayley graphs of various well-known groups. This has spawned a considerable amount of activity in the study of the combinatorial properties of such graphs. A number of symposia and congresses (such as the bi-annual IWIN, starting in 1991) bear witness to the interest of the computer science community in this subject. On the mathematical side, and independently of any interest in applications, progress in group theory has made it possible to make a realistic attempt at a complete description of vertex-transitive graphs. The classification of the finite simple groups has played an important role in this respect.
Author: Cheryl E. Praeger
Publisher: London Mathematical Society Le
ISBN: 0521675065
Category : Mathematics
Languages : en
Pages : 338
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Book Description
Concise introduction to permutation groups, focusing on invariant cartesian decompositions and applications in algebra and combinatorics.
Author: Martin W. Liebeck
Publisher: American Mathematical Soc.
ISBN: 0821824945
Category : Mathematics
Languages : en
Pages : 161
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Book Description
The main result describes completely the maximal factorizations of all the finite simple groups and their automorphism groups. As a consequence, a classification of the maximal subgroups of the finite alternating and symmetric groups is obtained.
Author: Bertram Huppert
Publisher: Walter de Gruyter
ISBN: 3110809230
Category : Mathematics
Languages : en
Pages : 625
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Book Description
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
