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Structure Theory for Canonical Classes of Finite Groups

Author: Wenbin Guo

Publisher: Springer

Published: 2015-04-23

Total Pages: 369

ISBN-13: 3662457474

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

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.

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 It introduces some unpublished and fundamental advances in this Theory and provides a new insight into some classic facts in this area.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.

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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The Seventh European Conference on Combinatorics, Graph Theory and Applications

Author: Jaroslav Nešetřil

Publisher: Springer Science & Business Media

Published: 2014-01-18

Total Pages: 600

ISBN-13: 887642475X

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In the tradition of EuroComb'01 (Barcelona), Eurocomb'03 (Prague), EuroComb'05 (Berlin), Eurocomb'07 (Seville), Eurocomb'09 (Bordeaux), and Eurocomb'11 (Budapest), this volume covers recent advances in combinatorics and graph theory including applications in other areas of mathematics, computer science and engineering. Topics include, but are not limited to: Algebraic combinatorics, combinatorial geometry, combinatorial number theory, combinatorial optimization, designs and configurations, enumerative combinatorics, extremal combinatorics, ordered sets, random methods, topological combinatorics.

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.

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.

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.

Finite Groups

Author: Bertram A. F. Wehrfritz

Publisher: World Scientific

Published: 1999

Total Pages: 138

ISBN-13: 9789810238742

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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 Collected Papers of William Burnside: Commentary on Burnside's life and work ; Papers 1883-1899

Author: William Burnside

Publisher:

Published: 2004

Total Pages: 818

ISBN-13: 9780198505860

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William Burnside was one of the three most important algebraists who were involved in the transformation of group theory from its nineteenth-century origins to a deep twentieth-century subject. Building on work of earlier mathematicians, they were able to develop sophisticated tools for solving difficult problems. All of Burnside's papers are reproduced here, organized chronologically and with a detailed bibliography. Walter Feit has contributed a foreword, and a collection of introductory essays are included to provide a commentary on Burnside's work and set it in perspective along with a modern biography that draws on archive material.