The Theory of Classes of Groups

Author: Guo Wenbin

Publisher: Springer Science & Business Media

ISBN: 9401140545

Category: Mathematics

Page: 258

View: 2167

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One of the characteristics of modern algebra is the development of new tools and concepts for exploring classes of algebraic systems, whereas the research on individual algebraic systems (e. g. , groups, rings, Lie algebras, etc. ) continues along traditional lines. The early work on classes of alge bras was concerned with showing that one class X of algebraic systems is actually contained in another class F. Modern research into the theory of classes was initiated in the 1930's by Birkhoff's work [1] on general varieties of algebras, and Neumann's work [1] on varieties of groups. A. I. Mal'cev made fundamental contributions to this modern development. ln his re ports [1, 3] of 1963 and 1966 to The Fourth All-Union Mathematics Con ference and to another international mathematics congress, striking the ories of classes of algebraic systems were presented. These were later included in his book [5]. International interest in the theory of formations of finite groups was aroused, and rapidly heated up, during this time, thanks to the work of Gaschiitz [8] in 1963, and the work of Carter and Hawkes [1] in 1967. The major topics considered were saturated formations, Fitting classes, and Schunck classes. A class of groups is called a formation if it is closed with respect to homomorphic images and subdirect products. A formation is called saturated provided that G E F whenever Gjip(G) E F.
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Structure Theory for Canonical Classes of Finite Groups

Author: Wenbin Guo

Publisher: Springer

ISBN: 3662457474

Category: Mathematics

Page: 359

View: 1531

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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.
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A Course in the Theory of Groups

Author: Derek J.S. Robinson

Publisher: Springer Science & Business Media

ISBN: 1441985948

Category: Mathematics

Page: 502

View: 2270

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"An excellent up-to-date introduction to the theory of groups. It is general yet comprehensive, covering various branches of group theory. The 15 chapters contain the following main topics: free groups and presentations, free products, decompositions, Abelian groups, finite permutation groups, representations of groups, finite and infinite soluble groups, group extensions, generalizations of nilpotent and soluble groups, finiteness properties." —-ACTA SCIENTIARUM MATHEMATICARUM
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Products of Finite Groups

Author: Adolfo Ballester-Bolinches,Ramon Esteban-Romero,Mohamed Asaad

Publisher: Walter de Gruyter

ISBN: 3110204177

Category: Mathematics

Page: 334

View: 5331

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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.
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Abstract Algebra with Applications

Volume 1: Vector Spaces and Groups

Author: Karlheinz Spindler

Publisher: CRC Press

ISBN: 9780824791445

Category: Mathematics

Page: 776

View: 2522

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A comprehensive presentation of abstract algebra and an in-depth treatment of the applications of algebraic techniques and the relationship of algebra to other disciplines, such as number theory, combinatorics, geometry, topology, differential equations, and Markov chains.
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The Theory and Applications of Harmonic Integrals

Author: W. V. D. Hodge

Publisher: CUP Archive

ISBN: 9780521358811

Category: Mathematics

Page: 284

View: 2537

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First published in 1941, this book, by one of the foremost geometers of his day, rapidly became a classic. In its original form the book constituted a section of Hodge's essay for which the Adam's prize of 1936 was awarded, but the author substantially revised and rewrote it. The book begins with an exposition of the geometry of manifolds and the properties of integrals on manifolds. The remainder of the book is then concerned with the application of the theory of harmonic integrals to other branches of mathematics, particularly to algebraic varieties and to continuous groups. Differential geometers and workers in allied subjects will welcome this reissue both for its lucid account of the subject and for its historical value. For this paperback edition, Professor Sir Michael Atiyah has written a foreword that sets Hodges work in its historical context and relates it briefly to developments.
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Classes of Finite Groups

Author: Adolfo Ballester-Bolinches,Luis M. Ezquerro

Publisher: Springer Science & Business Media

ISBN: 1402047193

Category: Mathematics

Page: 381

View: 2795

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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.
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Semigroup Theory and Its Applications

Proceedings of the 1994 Conference Commemorating the Work of Alfred H. Clifford

Author: Alfred Hoblitzelle Clifford

Publisher: Cambridge University Press

ISBN: 9780521576697

Category: Mathematics

Page: 165

View: 3310

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Survey articles in the area of semigroup theory and its applications.
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Representations and Characters of Finite Groups

Author: M. J. Collins,Dr Michael J Collins, M.D,Michael J. Stratford-Collins

Publisher: Cambridge University Press

ISBN: 9780521234405

Category: Mathematics

Page: 242

View: 2067

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Representation theory and character theory have proved essential in the study of finite simple groups since their early development by Frobenius. The author begins by presenting the foundations of character theory in a style accessible to advanced undergraduates that requires only a basic knowledge of group theory and general algebra. This theme is then expanded in a self-contained account providing an introduction to the application of character theory to the classification of simple groups. The book follows both strands of the theory: the exceptional characteristics of Suzuki and Feit and the block character theory of Brauer and includes refinements of original proofs that have become available as the subject has grown.
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