The Classification Of The Finite Simple Groups Number 9
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The Classification Of The Finite Simple Groups Number 5
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Author : Daniel Gorenstein
language : en
Publisher: American Mathematical Soc.
Release Date : 1994
The Classification Of The Finite Simple Groups Number 5 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 fifth volume of the study proves two, and part of the third, of the planned five stages for the generic cast of the classification of finite simple groups. The main result is that either G has a p-uniqueness subgroup for some prime p, or that G has a neighborhood of semisimple subgroups that demonstrate certain properties in common with those in target simple groups G*. All this is preparation for the final stages, which are expected to deduce that G is about the same as G* for some known simple G*. Stay tuned. Perhaps an index will be deemed meet when the final answers are revealed. Annotation copyrighted by Book News, Inc., Portland, OR
The Classification Of The Finite Simple Groups Number 9
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Author : Inna Capdeboscq
language : en
Publisher: American Mathematical Society
Release Date : 2021-02-22
The Classification Of The Finite Simple Groups Number 9 written by Inna Capdeboscq and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-22 with Mathematics categories.
This book is the ninth volume in a series whose goal is to furnish a careful and largely self-contained proof of the classification theorem for the finite simple groups. Having completed the classification of the simple groups of odd type as well as the classification of the simple groups of generic even type (modulo uniqueness theorems to appear later), the current volume begins the classification of the finite simple groups of special even type. The principal result of this volume is a classification of the groups of bicharacteristic type, i.e., of both even type and of $p$-type for a suitable odd prime $p$. It is here that the largest sporadic groups emerge, namely the Monster, the Baby Monster, the largest Conway group, and the three Fischer groups, along with six finite groups of Lie type over small fields, several of which play a major role as subgroups or sections of these sporadic groups.
The Classification Of Finite Simple Groups
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Author : Michael Aschbacher
language : en
Publisher: American Mathematical Soc.
Release Date : 2011
The Classification Of Finite Simple Groups written by Michael Aschbacher 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 2011 with Mathematics categories.
Provides an outline and modern overview of the classification of the finite simple groups. It primarily covers the 'even case', where the main groups arising are Lie-type (matrix) groups over a field of characteristic 2. The book thus completes a project begun by Daniel Gorenstein's 1983 book, which outlined the classification of groups of 'noncharacteristic 2 type'.
Finite Simple Groups
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Author : Daniel Gorenstein
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-27
Finite Simple Groups written by Daniel Gorenstein 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 2013-11-27 with Mathematics categories.
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.
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].
The Classification Of The Finite Simple Groups Number 8
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Author : Daniel Gorenstein
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-12-12
The Classification Of The Finite Simple Groups Number 8 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 2018-12-12 with Mathematics categories.
This book completes a trilogy (Numbers 5, 7, and 8) of the series The Classification of the Finite Simple Groups treating the generic case of the classification of the finite simple groups. In conjunction with Numbers 4 and 6, it allows us to reach a major milestone in our series—the completion of the proof of the following theorem: Theorem O: Let G be a finite simple group of odd type, all of whose proper simple sections are known simple groups. Then either G is an alternating group or G is a finite group of Lie type defined over a field of odd order or G is one of six sporadic simple groups. Put another way, Theorem O asserts that any minimal counterexample to the classification of the finite simple groups must be of even type. The work of Aschbacher and Smith shows that a minimal counterexample is not of quasithin even type, while this volume shows that a minimal counterexample cannot be of generic even type, modulo the treatment of certain intermediate configurations of even type which will be ruled out in the next volume of our series.
The Classification Of The Finite Simple Groups Number 4
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Author : Daniel Gorenstein
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
The Classification Of The Finite Simple Groups Number 4 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 1999 with Finite simple groups categories.
Finite And Locally Finite Groups
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Author : B. Hartley
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Finite And Locally Finite Groups written by B. Hartley 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.
This volume contains the proceedings of the NATO Advanced Study Institute on Finite and Locally Finite Groups held in Istanbul, Turkey, 14-27 August 1994, at which there were about 90 participants from some 16 different countries. The ASI received generous financial support from the Scientific Affairs Division of NATO. INTRODUCTION A locally finite group is a group in which every finite set of elements is contained in a finite subgroup. The study of locally finite groups began with Schur's result that a periodic linear group is, in fact, locally finite. The simple locally finite groups are of particular interest. In view of the classification of the finite simple groups and advances in representation theory, it is natural to pursue classification theorems for simple locally finite groups. This was one of the central themes of the Istanbul conference and significant progress is reported herein. The theory of simple locally finite groups intersects many areas of group theory and representation theory, so this served as a focus for several articles in the volume. Every simple locally finite group has what is known as a Kegel cover. This is a collection of pairs {(G , Ni) liE I}, where I is an index set, each group Gi is finite, i Ni
The Classification Of The Finite Simple Groups Number 6
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Author : Daniel Gorenstein
language : en
Publisher: American Mathematical Soc.
Release Date : 1994
The Classification Of The Finite Simple Groups Number 6 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 Computers categories.
The classification of finite simple groups is a landmark result of modern mathematics. This work presents critical aspects of the classification. It provides the classification of finite simple groups of special odd type (Theorems $\mathcal{C}_2$ and $\mathcal{C}_3$). It is suitable for graduate students and researchers interested in group theory.
The Classification Of Finite Simple Groups
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Author : Daniel Gorenstein
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-22
The Classification Of Finite Simple Groups written by Daniel Gorenstein 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 2013-11-22 with Mathematics categories.
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.