[PDF] Notes On Minimal Faithful Permutation Representations Of Finite Groups eBook

Author : Olaf Manz
Publisher : Cambridge University Press
Page : 318 pages
File Size : 44,24 MB
Release : 1993-09-16
Category : Mathematics
ISBN : 0521397391

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Representation theory plays an important role in algebra, and in this book Manz and Wolf concentrate on that part of the theory which relates to solvable groups. The authors begin by studying modules over finite fields, which arise naturally as chief factors of solvable groups. The information obtained can then be applied to infinite modules, and in particular to character theory (ordinary and Brauer) of solvable groups. The authors include proofs of Brauer's height zero conjecture and the Alperin-McKay conjecture for solvable groups. Gluck's permutation lemma and Huppert's classification of solvable two-transive permutation groups, which are essentially results about finite modules of finite groups, play important roles in the applications and a new proof is given of the latter. Researchers into group theory, representation theory, or both, will find that this book has much to offer.

Author : Benjamin Steinberg
Publisher : Springer Science & Business Media
Page : 166 pages
File Size : 44,71 MB
Release : 2011-10-23
Category : Mathematics
ISBN : 1461407761

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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 : Helmut Wielandt
Publisher : Academic Press
Page : 125 pages
File Size : 30,24 MB
Release : 2014-05-10
Category : Mathematics
ISBN : 1483258297

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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 : C. Musili
Publisher :
Page : 0 pages
File Size : 21,85 MB
Release : 2011
Category : Finite groups
ISBN : 9789380250182

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Provides an elementary introduction to the basic concepts of the theory of ordinary representations to finite groups with a minimum of prerequisites; explores the for the important special case of the symmetric groups $S_n$ of permutations on $n$ letters; and uses the preparatory material of the first two parts, coupled with the $S_n$ theory, to do the same for some other important special groups.

Author : Ambar N. Sengupta
Publisher : Springer Science & Business Media
Page : 383 pages
File Size : 25,81 MB
Release : 2011-12-09
Category : Mathematics
ISBN : 1461412315

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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.