Characters Of Solvable Groups
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Characters Of Solvable Groups
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Author : I. Martin Isaacs
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-05-23
Characters Of Solvable Groups written by I. Martin Isaacs and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-23 with Mathematics categories.
This book, which can be considered as a sequel of the author's famous book Character Theory of Finite Groups, concerns the character theory of finite solvable groups and other groups that have an abundance of normal subgroups. It is subdivided into three parts: -theory, character correspondences, and M-groups. The -theory section contains an exposition of D. Gajendragadkar's -special characters, and it includes various extensions, generalizations, and applications of his work. The character correspondences section proves the McKay character counting conjecture and the Alperin weight conjecture for solvable groups, and it constructs a canonical McKay bijection for odd-order groups. In addition to a review of some basic material on M-groups, the third section contains an exposition of the use of symplectic modules for studying M-groups. In particular, an accessible presentation of E. C. Dade's deep results on monomial characters of odd prime-power degree is included. Very little of this material has previously appeared in book form, and much of it is based on the author's research. By reading a clean and accessible presentation written by the leading expert in the field, researchers and graduate students will be inspired to learn and work in this area that has fascinated the author for decades.
Characters Of Solvable Groups
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Author : I. Martin Isaacs
language : en
Publisher:
Release Date : 2018
Characters Of Solvable Groups written by I. Martin Isaacs and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with MATHEMATICS categories.
This book, which can be considered as a sequel of the author's famous book Character Theory of Finite Groups, concerns the character theory of finite solvable groups and other groups that have an abundance of normal subgroups. It is subdivided into three parts: \pi-theory, character correspondences, and M-groups. The \pi-theory section contains an exposition of D. Gajendragadkar's \pi-special characters, and it includes various extensions, generalizations, and applications of his work. The character correspondences section proves the McKay character counting conjecture and the Alperin weight c.
Characters And Blocks Of Solvable Groups
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Author : James Cossey
language : en
Publisher: Springer Nature
Release Date : 2024-04-12
Characters And Blocks Of Solvable Groups written by James Cossey and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-12 with Mathematics categories.
This book highlights recent developments in the representation theory of finite solvable groups, which seeks to connect group theory to linear algebra in ways that allow for better study of the groups in question. Over the last several decades, a number of results in the representations of solvable groups have been proven using so-called “large orbit” theorems. This book provides an extensive survey of the current state of the large-orbit theorems. The authors outline the proofs of the large orbit theorems to provide an overview of the topic, then demonstrate how these theorems can be used to prove new results about solvable groups.
Generalized Permutation Characters Of Solvable Groups
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Author : Alan E. Parks
language : en
Publisher:
Release Date : 1982
Generalized Permutation Characters Of Solvable Groups written by Alan E. Parks and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Characters of groups categories.
Character Theory Of Finite Groups
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Author : I. Martin Isaacs
language : en
Publisher: American Mathematical Soc.
Release Date : 2006-11-21
Character Theory Of Finite Groups written by I. Martin Isaacs and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-21 with Mathematics categories.
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.
Representations Of Solvable Groups
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Author : Olaf Manz
language : en
Publisher: Cambridge University Press
Release Date : 1993-09-16
Representations Of Solvable Groups written by Olaf Manz and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-09-16 with Mathematics categories.
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.
Characters Of Finite Groups Part 1
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Author : IA. G. Berkovich E. M. Zhmud'
language : en
Publisher: American Mathematical Soc.
Release Date : 1997-12-02
Characters Of Finite Groups Part 1 written by IA. G. Berkovich E. M. Zhmud' and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-12-02 with categories.
This book discusses character theory and its applications to finite groups. The work places the subject within the reach of people with a relatively modest mathematical background. The necessary background exceeds the standard algebra course with respect only to finite groups. Starting with basic notions and theorems in character theory, the authors present a variety of results on the properties of complex-valued characters and applications to finite groups. The main themes are degrees and kernels of irreducible characters, the class number and the number of nonlinear irreducible characters, values of irreducible characters, characterizations and generalizations of Frobenius groups, and generalizations and applications of monomial groups. The presentation is detailed, and many proofs of known results are new. Most of the results in the book are presented in monograph form for the first time. Numerous exercises offer additional information on the topics and help readers to understand the main concepts and results.
Characters Of Finite Groups
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Author : I_A. G. Berkovich
language : en
Publisher: American Mathematical Soc.
Release Date : 1998-09-29
Characters Of Finite Groups written by I_A. G. Berkovich and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-09-29 with Mathematics categories.
This book places character theory and its applications to finite groups within the reach of people with a comparatively modest mathematical background. The work concentrates mostly on applications of character theory to finite groups. The main themes are degrees and kernels of irreducible characters, the class number and the number of nonlinear irreducible characters, values of irreducible characters, characterizations and generalizations of Frobenius groups, and generalizations of monomial groups. The presentation is detailed, and many proofs of known results are new.
Character Theory Of Finite Groups
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Author : Bertram Huppert
language : en
Publisher: Walter de Gruyter
Release Date : 2011-04-20
Character Theory Of Finite Groups written by Bertram Huppert and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04-20 with Mathematics categories.
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