Classes Of Finite Groups PDF Download
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Author | : Adolfo Ballester-Bolinches |
Publisher | : Springer Science & Business Media |
Total Pages | : 391 |
Release | : 2006-07-10 |
Genre | : Mathematics |
ISBN | : 1402047193 |
Download Classes of Finite Groups Book in PDF, ePub and Kindle
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 It introduces some unpublished and fundamental advances in this Theory and provides a new insight into some classic facts in this area.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.
Author | : Wenbin Guo |
Publisher | : Springer |
Total Pages | : 369 |
Release | : 2015-04-23 |
Genre | : Mathematics |
ISBN | : 3662457474 |
Download Structure Theory for Canonical Classes of Finite Groups Book in PDF, ePub and Kindle
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.
Author | : Guo Wenbin |
Publisher | : Springer Science & Business Media |
Total Pages | : 270 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 9401140545 |
Download The Theory of Classes of Groups Book in PDF, ePub and Kindle
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.
Author | : Daniel Gorenstein |
Publisher | : Springer Science & Business Media |
Total Pages | : 339 |
Release | : 2013-11-27 |
Genre | : Mathematics |
ISBN | : 1468484974 |
Download Finite Simple Groups Book in PDF, ePub and Kindle
In February 1981, the classification of the finite simple groups (Dl)* was completed,t. * representing one of the most remarkable achievements in the history or mathematics. Involving the combined efforts of several hundred mathematicians from around the world over a period of 30 years, the full proof covered something between 5,000 and 10,000 journal pages, spread over 300 to 500 individual papers. The single result that, more than any other, opened up the field and foreshadowed the vastness of the full classification proof was the celebrated theorem of Walter Feit and John Thompson in 1962, which stated that every finite group of odd order (D2) is solvable (D3)-a statement expressi ble in a single line, yet its proof required a full 255-page issue of the Pacific 10urnal of Mathematics [93]. Soon thereafter, in 1965, came the first new sporadic simple group in over 100 years, the Zvonimir Janko group 1 , to further stimulate the 1 'To make the book as self-contained as possible. we are including definitions of various terms as they occur in the text. However. in order not to disrupt the continuity of the discussion. we have placed them at the end of the Introduction. We denote these definitions by (DI). (D2), (D3). etc.
Author | : Armand Borel |
Publisher | : Springer |
Total Pages | : 329 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 354036272X |
Download Seminar on Algebraic Groups and Related Finite Groups Book in PDF, ePub and Kindle
Author | : François Digne |
Publisher | : Cambridge University Press |
Total Pages | : 267 |
Release | : 2020-03-05 |
Genre | : Mathematics |
ISBN | : 1108481485 |
Download Representations of Finite Groups of Lie Type Book in PDF, ePub and Kindle
An up-to-date and self-contained introduction based on a graduate course taught at the University of Paris.
Author | : Peter Webb |
Publisher | : Cambridge University Press |
Total Pages | : 339 |
Release | : 2016-08-19 |
Genre | : Mathematics |
ISBN | : 1107162394 |
Download A Course in Finite Group Representation Theory Book in PDF, ePub and Kindle
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.
Author | : Daniel Gorenstein |
Publisher | : American Mathematical Soc. |
Total Pages | : 186 |
Release | : 1994-11-18 |
Genre | : Mathematics |
ISBN | : 0821809601 |
Download The Classification of the Finite Simple Groups Book in PDF, ePub and Kindle
The classification of the finite simple groups is one of the major feats of contemporary mathematical research, but its proof has never been completely extricated from the journal literature in which it first appeared. This book serves as an introduction to a series devoted to organizing and simplifying the proof. The purpose of the series is to present as direct and coherent a proof as is possible with existing techniques. This first volume, which sets up the structure for the entire series, begins with largely informal discussions of the relationship between the Classification Theorem and the general structure of finite groups, as well as the general strategy to be followed in the series and a comparison with the original proof. Also listed are background results from the literature that will be used in subsequent volumes. Next, the authors formally present the structure of the proof and the plan for the series of volumes in the form of two grids, giving the main case division of the proof as well as the principal milestones in the analysis of each case. Thumbnail sketches are given of the ten or so principal methods underlying the proof. Much of the book is written in an expository style accessible to nonspecialists.
Author | : Bertram A. F. Wehrfritz |
Publisher | : World Scientific |
Total Pages | : 138 |
Release | : 1999 |
Genre | : Mathematics |
ISBN | : 9789810238742 |
Download Finite Groups Book in PDF, ePub and Kindle
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.
Author | : Daniel Gorenstein |
Publisher | : Springer Science & Business Media |
Total Pages | : 493 |
Release | : 2013-11-22 |
Genre | : Mathematics |
ISBN | : 1461336856 |
Download The Classification of Finite Simple Groups Book in PDF, ePub and Kindle
Never before in the history of mathematics has there been an individual theorem whose proof has required 10,000 journal pages of closely reasoned argument. Who could read such a proof, let alone communicate it to others? But the classification of all finite simple groups is such a theorem-its complete proof, developed over a 30-year period by about 100 group theorists, is the union of some 500 journal articles covering approximately 10,000 printed pages. How then is one who has lived through it all to convey the richness and variety of this monumental achievement? Yet such an attempt must be made, for without the existence of a coherent exposition of the total proof, there is a very real danger that it will gradually become lost to the living world of mathematics, buried within the dusty pages of forgotten journals. For it is almost impossible for the uninitiated to find the way through the tangled proof without an experienced guide; even the 500 papers themselves require careful selection from among some 2,000 articles on simple group theory, which together include often attractive byways, but which serve only to delay the journey.