Finite Groups Iii
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Finite Groups Iii
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Author : B. Huppert
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Finite Groups Iii written by B. Huppert and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Und dann erst kommt der "Ab -ge - sa. ng\' da. /3 der nidlt kurz und nicht zu la. ng, From "Die Meistersinger von Nürnberg", Richard Wagner This final volume is concerned with some of the developments of the subject in the 1960's. In attempting to determine the simple groups, the first step was to settle the conjecture of Burnside that groups of odd order are soluble. The proof that this conjecture was correct is much too long and complicated for presentation in this text, but a number of ideas in the early stages of it led to a local theory of finite groups, so me aspects of which are discussed in Chapter X. Much of this discussion is a con tinuation of the theory of the transfer (see Chapter IV), but we also introduce the generalized Fitting subgroup, which played a basic role in characterization theorems, that is, in descriptions of specific groups in terms of group-theoretical properties alone. One of the earliest and most important such characterizations was given for Zassenhaus groups; this is presented in Chapter XI. Characterizations in terms of the centralizer of an involution are of particular importance in view of the theorem of Brauer and Fowler. In Chapter XII, one such theorem is given, in which the Mathieu group 9J'l1l and PSL(3, 3) are characterized
Finite Groups Ii
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Author : B. Huppert
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Finite Groups Ii written by B. Huppert and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
17):~t? L It CIFDr- ! wei! unsre Weisheit Einfalt ist, From "Lohengrin", Richard Wagner At the time of the appearance of the first volume of this work in 1967, the tempestuous development of finite group theory had already made it virtually impossible to give a complete presentation of the subject in one treatise. The present volume and its successor have therefore the more modest aim of giving descriptions of the recent development of certain important parts of the subject, and even in these parts no attempt at completeness has been made. Chapter VII deals with the representation theory of finite groups in arbitrary fields with particular attention to those of non-zero charac teristic. That part of modular representation theory which is essentially the block theory of complex characters has not been included, as there are already monographs on this subject and others will shortly appear. Instead, we have restricted ourselves to such results as can be obtained by purely module-theoretical means.
The Classification Of The Finite Simple Groups Number 2
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Author : Daniel Gorenstein
language : en
Publisher: American Mathematical Soc.
Release Date : 1994
The Classification Of The Finite Simple Groups Number 2 written by Daniel Gorenstein 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 1994 with Mathematics categories.
The second volume of a series devoted to reorganizing and simplifying proof of the classification of the finite simple groups. In a single chapter, it lays the groundwork for the forthcoming analysis of finite simple groups, beginning with the theory of components, layers, and the generalized Fitting subgroup, which has been developed largely since Gorenstein's basic 1968 text and is now central to understanding the structure of finite groups. Suitable as an auxiliary text for a graduate course in group theory. Member prices are $35 for individual and $47 for institutions. Annotation copyright by Book News, Inc., Portland, OR
Classes Of Finite Groups
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Author : Adolfo Ballester-Bolinches
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-07-10
Classes Of Finite Groups written by Adolfo Ballester-Bolinches and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-07-10 with Mathematics categories.
Many group theorists all over the world have been trying in the last twenty-five years to extend and adapt the magnificent methods of the Theory of Finite Soluble Groups to the more ambitious universe of all finite groups. This is a natural progression after the classification of finite simple groups but the achievements in this area are scattered in various papers. Our objectives in this book were to gather, order and examine all this material, including the latest advances made, give a new approach to some classic topics, shed light on some fundamental facts that still remain unpublished and present some new subjects of research in the theory of classes of finite, not necessarily solvable, groups.
A Course On Finite Groups
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Author : H.E. Rose
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-12-16
A Course On Finite Groups written by H.E. Rose and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-12-16 with Mathematics categories.
Introduces the richness of group theory to advanced undergraduate and graduate students, concentrating on the finite aspects. Provides a wealth of exercises and problems to support self-study. Additional online resources on more challenging and more specialised topics can be used as extension material for courses, or for further independent study.
Structure Theory For Canonical Classes Of Finite Groups
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Author : Wenbin Guo
language : en
Publisher: Springer
Release Date : 2015-04-23
Structure Theory For Canonical Classes Of Finite Groups written by Wenbin Guo and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-23 with Mathematics categories.
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.
Representation Theory Of Finite Groups A Guidebook
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Author : David A. Craven
language : en
Publisher: Springer Nature
Release Date : 2019-08-30
Representation Theory Of Finite Groups A Guidebook written by David A. Craven and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-30 with Mathematics categories.
This book provides an accessible introduction to the state of the art of representation theory of finite groups. Starting from a basic level that is summarized at the start, the book proceeds to cover topics of current research interest, including open problems and conjectures. The central themes of the book are block theory and module theory of group representations, which are comprehensively surveyed with a full bibliography. The individual chapters cover a range of topics within the subject, from blocks with cyclic defect groups to representations of symmetric groups. Assuming only modest background knowledge at the level of a first graduate course in algebra, this guidebook, intended for students taking first steps in the field, will also provide a reference for more experienced researchers. Although no proofs are included, end-of-chapter exercises make it suitable for student seminars.
Profinite Groups
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Author : Luis Ribes
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-03-10
Profinite Groups written by Luis Ribes and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-03-10 with Mathematics categories.
The aim of this book is to serve both as an introduction to profinite groups and as a reference for specialists in some areas of the theory. The book is reasonably self-contained. Profinite groups are Galois groups. As such they are of interest in algebraic number theory. Much of recent research on abstract infinite groups is related to profinite groups because residually finite groups are naturally embedded in a profinite group. In addition to basic facts about general profinite groups, the book emphasizes free constructions (particularly free profinite groups and the structure of their subgroups). Homology and cohomology is described with a minimum of prerequisites. This second edition contains three new appendices dealing with a new characterization of free profinite groups, presentations of pro-p groups and a new conceptually simpler approach to the proof of some classical subgroup theorems. Throughout the text there are additions in the form of new results, improved proofs, typographical corrections, and an enlarged bibliography. The list of open questions has been updated; comments and references have been added about those previously open problems that have been solved after the first edition appeared.
The Finite Simple Groups
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Author : Robert Wilson
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-12-14
The Finite Simple Groups written by Robert Wilson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-12-14 with Mathematics categories.
Thisbookisintendedasanintroductiontoallthe?nitesimplegroups.During themonumentalstruggletoclassifythe?nitesimplegroups(andindeedsince), a huge amount of information about these groups has been accumulated. Conveyingthisinformationtothenextgenerationofstudentsandresearchers, not to mention those who might wish to apply this knowledge, has become a major challenge. With the publication of the two volumes by Aschbacher and Smith [12, 13] in 2004 we can reasonably regard the proof of the Classi?cation Theorem for Finite Simple Groups (usually abbreviated CFSG) as complete. Thus it is timely to attempt an overview of all the (non-abelian) ?nite simple groups in one volume. For expository purposes it is convenient to divide them into four basic types, namely the alternating, classical, exceptional and sporadic groups. The study of alternating groups soon develops into the theory of per- tation groups, which is well served by the classic text of Wielandt [170]and more modern treatments such as the comprehensive introduction by Dixon and Mortimer [53] and more specialised texts such as that of Cameron [19].