Structure Theory for Canonical Classes of Finite Groups

Structure Theory for Canonical Classes of Finite Groups

Author: Wenbin Guo

Publisher: Springer

Published: 2015-04-23

Total Pages: 369

ISBN-13: 3662457474

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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.


Book Synopsis Structure Theory for Canonical Classes of Finite Groups by : Wenbin Guo

Download or read book Structure Theory for Canonical Classes of Finite Groups written by Wenbin Guo and published by Springer. This book was released on 2015-04-23 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

A Course in Finite Group Representation Theory

A Course in Finite Group Representation Theory

Author: Peter Webb

Publisher: Cambridge University Press

Published: 2016-08-19

Total Pages: 339

ISBN-13: 1107162394

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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.


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.

Classes of Finite Groups

Classes of Finite Groups

Author: Adolfo Ballester-Bollinches

Publisher: Springer

Published: 2009-09-03

Total Pages: 381

ISBN-13: 9789048108329

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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.


Book Synopsis Classes of Finite Groups by : Adolfo Ballester-Bollinches

Download or read book Classes of Finite Groups written by Adolfo Ballester-Bollinches and published by Springer. This book was released on 2009-09-03 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Classes of Finite Groups

Classes of Finite Groups

Author: Adolfo Ballester-Bolinches

Publisher: Springer Science & Business Media

Published: 2006-07-10

Total Pages: 391

ISBN-13: 1402047193

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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.


Book Synopsis Classes of Finite Groups by : Adolfo Ballester-Bolinches

Download or read book Classes of Finite Groups written by Adolfo Ballester-Bolinches and published by Springer Science & Business Media. This book was released on 2006-07-10 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Representation Theory of Finite Groups

Representation Theory of Finite Groups

Author: Benjamin Steinberg

Publisher: Springer Science & Business Media

Published: 2011-10-23

Total Pages: 166

ISBN-13: 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.


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.

Representation Theory of Finite Groups and Finite-Dimensional Algebras

Representation Theory of Finite Groups and Finite-Dimensional Algebras

Author: Michler

Publisher: Birkhäuser

Published: 2012-12-06

Total Pages: 526

ISBN-13: 3034886586

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From April 1, 1984 until March 31, 1991 the Deutsche Forschungsgemeinschaft has sponsored the project "Representation Theory of Finite Groups and Finite Di mensional Algebras". The proposal for this project was submitted by B. Huppert (Mainz), B. Fischer (Bielefeld), G. Michler (Essen), H. Pahlings (Aachen) and C. M. Ringel (Bielefeld) in order to strengthen the interaction between the different re search areas in representation theory. The Deutsche Forschungsgemeinschaft has given many research positions and fellowships for young algebraists enabling them to do research at their own uni versities or as visitors at well known research institutions in America, Australia, England and France. The whole project benefitted very much from an extensive exchange programme between German and American scientists sponsored by the Deutsche Forschungsgemeinschaft and by the National Science Foundation of the United States. This volume presents lectures given in a final conference and reports by members of the project. It is divided into two parts. The first part contains seven survey articles describing recent advances in different areas of representation theory. These articles do not only concentrate on the work done by the German research groups, but also inform on major developments of the subject at all. The volume omits those topics already treated in book form. In particular, it does not contain a survey on K.


Book Synopsis Representation Theory of Finite Groups and Finite-Dimensional Algebras by : Michler

Download or read book Representation Theory of Finite Groups and Finite-Dimensional Algebras written by Michler and published by Birkhäuser. This book was released on 2012-12-06 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: From April 1, 1984 until March 31, 1991 the Deutsche Forschungsgemeinschaft has sponsored the project "Representation Theory of Finite Groups and Finite Di mensional Algebras". The proposal for this project was submitted by B. Huppert (Mainz), B. Fischer (Bielefeld), G. Michler (Essen), H. Pahlings (Aachen) and C. M. Ringel (Bielefeld) in order to strengthen the interaction between the different re search areas in representation theory. The Deutsche Forschungsgemeinschaft has given many research positions and fellowships for young algebraists enabling them to do research at their own uni versities or as visitors at well known research institutions in America, Australia, England and France. The whole project benefitted very much from an extensive exchange programme between German and American scientists sponsored by the Deutsche Forschungsgemeinschaft and by the National Science Foundation of the United States. This volume presents lectures given in a final conference and reports by members of the project. It is divided into two parts. The first part contains seven survey articles describing recent advances in different areas of representation theory. These articles do not only concentrate on the work done by the German research groups, but also inform on major developments of the subject at all. The volume omits those topics already treated in book form. In particular, it does not contain a survey on K.

Products of Finite Groups

Products of Finite Groups

Author: Adolfo Ballester-Bolinches

Publisher: Walter de Gruyter

Published: 2010-10-19

Total Pages: 347

ISBN-13: 311022061X

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The study of finite groups factorised as a product of two or more subgroups has become a subject of great interest during the last years with applications not only in group theory, but also in other areas like cryptography and coding theory. It has experienced a big impulse with the introduction of some permutability conditions. The aim of this book is to gather, order, and examine part of this material, including the latest advances made, give some new approach to some topics, and present some new subjects of research in the theory of finite factorised groups. Some of the topics covered by this book include groups whose subnormal subgroups are normal, permutable, or Sylow-permutable, products of nilpotent groups, and an exhaustive structural study of totally and mutually permutable products of finite groups and their relation with classes of groups. This monograph is mainly addressed to graduate students and senior researchers interested in the study of products and permutability of finite groups. A background in finite group theory and a basic knowledge of representation theory and classes of groups is recommended to follow it.


Book Synopsis Products of Finite Groups by : Adolfo Ballester-Bolinches

Download or read book Products of Finite Groups written by Adolfo Ballester-Bolinches and published by Walter de Gruyter. This book was released on 2010-10-19 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of finite groups factorised as a product of two or more subgroups has become a subject of great interest during the last years with applications not only in group theory, but also in other areas like cryptography and coding theory. It has experienced a big impulse with the introduction of some permutability conditions. The aim of this book is to gather, order, and examine part of this material, including the latest advances made, give some new approach to some topics, and present some new subjects of research in the theory of finite factorised groups. Some of the topics covered by this book include groups whose subnormal subgroups are normal, permutable, or Sylow-permutable, products of nilpotent groups, and an exhaustive structural study of totally and mutually permutable products of finite groups and their relation with classes of groups. This monograph is mainly addressed to graduate students and senior researchers interested in the study of products and permutability of finite groups. A background in finite group theory and a basic knowledge of representation theory and classes of groups is recommended to follow it.

The Block Theory of Finite Group Algebras: Volume 2

The Block Theory of Finite Group Algebras: Volume 2

Author: Markus Linckelmann

Publisher: Cambridge University Press

Published: 2018-05-24

Total Pages: 523

ISBN-13: 1108562582

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This is a comprehensive introduction to the modular representation theory of finite groups, with an emphasis on block theory. The two volumes take into account classical results and concepts as well as some of the modern developments in the area. Volume 1 introduces the broader context, starting with general properties of finite group algebras over commutative rings, moving on to some basics in character theory and the structure theory of algebras over complete discrete valuation rings. In Volume 2, blocks of finite group algebras over complete p-local rings take centre stage, and many key results which have not appeared in a book before are treated in detail. In order to illustrate the wide range of techniques in block theory, the book concludes with chapters classifying the source algebras of blocks with cyclic and Klein four defect groups, and relating these classifications to the open conjectures that drive block theory.


Book Synopsis The Block Theory of Finite Group Algebras: Volume 2 by : Markus Linckelmann

Download or read book The Block Theory of Finite Group Algebras: Volume 2 written by Markus Linckelmann and published by Cambridge University Press. This book was released on 2018-05-24 with total page 523 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a comprehensive introduction to the modular representation theory of finite groups, with an emphasis on block theory. The two volumes take into account classical results and concepts as well as some of the modern developments in the area. Volume 1 introduces the broader context, starting with general properties of finite group algebras over commutative rings, moving on to some basics in character theory and the structure theory of algebras over complete discrete valuation rings. In Volume 2, blocks of finite group algebras over complete p-local rings take centre stage, and many key results which have not appeared in a book before are treated in detail. In order to illustrate the wide range of techniques in block theory, the book concludes with chapters classifying the source algebras of blocks with cyclic and Klein four defect groups, and relating these classifications to the open conjectures that drive block theory.

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

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

Author: Martyn Russell Dixon

Publisher: World Scientific

Published: 1994

Total Pages: 324

ISBN-13: 9789810217952

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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.


Book Synopsis Sylow Theory, Formations, and Fitting Classes in Locally Finite Groups by : Martyn Russell Dixon

Download or read book Sylow Theory, Formations, and Fitting Classes in Locally Finite Groups written by Martyn Russell Dixon and published by World Scientific. This book was released on 1994 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Block Theory of Finite Group Algebras:

The Block Theory of Finite Group Algebras:

Author: Markus Linckelmann

Publisher: Cambridge University Press

Published: 2018-05-24

Total Pages: 524

ISBN-13: 1108589219

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This is a comprehensive introduction to the modular representation theory of finite groups, with an emphasis on block theory. The two volumes take into account classical results and concepts as well as some of the modern developments in the area. Volume 1 introduces the broader context, starting with general properties of finite group algebras over commutative rings, moving on to some basics in character theory and the structure theory of algebras over complete discrete valuation rings. In Volume 2, blocks of finite group algebras over complete p-local rings take centre stage, and many key results which have not appeared in a book before are treated in detail. In order to illustrate the wide range of techniques in block theory, the book concludes with chapters classifying the source algebras of blocks with cyclic and Klein four defect groups, and relating these classifications to the open conjectures that drive block theory.


Book Synopsis The Block Theory of Finite Group Algebras: by : Markus Linckelmann

Download or read book The Block Theory of Finite Group Algebras: written by Markus Linckelmann and published by Cambridge University Press. This book was released on 2018-05-24 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a comprehensive introduction to the modular representation theory of finite groups, with an emphasis on block theory. The two volumes take into account classical results and concepts as well as some of the modern developments in the area. Volume 1 introduces the broader context, starting with general properties of finite group algebras over commutative rings, moving on to some basics in character theory and the structure theory of algebras over complete discrete valuation rings. In Volume 2, blocks of finite group algebras over complete p-local rings take centre stage, and many key results which have not appeared in a book before are treated in detail. In order to illustrate the wide range of techniques in block theory, the book concludes with chapters classifying the source algebras of blocks with cyclic and Klein four defect groups, and relating these classifications to the open conjectures that drive block theory.