The Classification Of The Finite Simple Groups Number 9
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The Classification Of The Finite Simple Groups Number 10
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Author : Inna Capdeboscq
language : en
Publisher: American Mathematical Society
Release Date : 2023-10-23
The Classification Of The Finite Simple Groups Number 10 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 2023-10-23 with Mathematics categories.
This book is the tenth in a series of volumes whose aim is to provide a complete proof of the classification theorem for the finite simple groups based on a fairly short and clearly enumerated set of background results. Specifically, this book completes our identification of the simple groups of bicharacteristic type begun in the ninth volume of the series (see SURV/40.9). This is a fascinating set of simple groups which have properties in common with matrix groups (or, more generally, groups of Lie type) defined both over fields of characteristic 2 and over fields of characteristic 3. This set includes 11 of the celebrated 26 sporadic simple groups along with several of their large simple subgroups. Together with SURV/40.9, this volume provides the first unified treatment of this class of simple groups.
The Classification Of The Finite Simple Groups
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Author : Inna Capdeboscq
language : en
Publisher:
Release Date : 2021
The Classification Of The Finite Simple Groups written by Inna Capdeboscq and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.
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 The Finite Simple Groups Number 3
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Author : Daniel Gorenstein
language : en
Publisher: American Mathematical Soc.
Release Date : 1994
The Classification Of The Finite Simple Groups Number 3 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 Finite simple groups categories.
Examines the internal structure of the finite simple groups of Lie type, the finite alternating groups, and 26 sporadic finite simple groups, as well as their analogues. Emphasis is on the structure of local subgroups and their relationships with one another, rather than development of an abstract theory of simple groups. A foundation is laid for the development of specific properties of K-groups to be used in the inductive proof of the classification theorem. Highlights include statements and proofs of the Breol-Tits and Curtis-Tits theorems, and material on centralizers of semisimple involutions in groups of Lie type. For graduate students and research mathematicians. Annotation copyrighted by Book News, Inc., Portland, OR
The Classification Of The Finite Simple Groups
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Author : Daniel Gorenstein
language : en
Publisher: American Mathematical Soc.
Release Date : 1994-11-18
The Classification Of The Finite Simple Groups 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 1994-11-18 with Mathematics categories.
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.
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.
The Classification Of The Finite Simple Groups Number 7 Part Iii Chapters 7 11 The Generic Case Stages 3b And 4a
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Author : Daniel Gorenstein
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-02-15
The Classification Of The Finite Simple Groups Number 7 Part Iii Chapters 7 11 The Generic Case Stages 3b And 4a 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 2018-02-15 with Finite simple groups categories.
The classification of finite simple groups is a landmark result of modern mathematics. The multipart series of monographs which is being published by the AMS (Volume 40.1–40.7 and future volumes) represents the culmination of a century-long project involving the efforts of scores of mathematicians published in hundreds of journal articles, books, and doctoral theses, totaling an estimated 15,000 pages. This part 7 of the series is the middle of a trilogy (Volume 40.5, Volume 40.7, and forthcoming Volume 40.8) treating the Generic Case, i.e., the identification of the alternating groups of degree at least 13 and most of the finite simple groups of Lie type and Lie rank at least 4. Moreover, Volumes 40.4–40.8 of this series will provide a complete treatment of the simple groups of odd type, i.e., the alternating groups (with two exceptions) and the groups of Lie type defined over a finite field of odd order, as well as some of the sporadic simple groups. In particular, this volume completes the construction, begun in Volume 40.5, of a collection of neighboring centralizers of a particularly nice form. All of this is then applied to complete the identification of the alternating groups of degree at least 13. The book is suitable for graduate students and researchers interested in the theory of finite groups.
The Classification Of The Finite Simple Groups Part V Chapters 9 17 Theorem C6 And Theorem C4 Case A
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Author : Daniel Gorenstein
language : en
Publisher:
Release Date : 1994
The Classification Of The Finite Simple Groups Part V Chapters 9 17 Theorem C6 And Theorem C4 Case A written by Daniel Gorenstein and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Finite simple groups categories.
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 Classification Of Finite Simple Groups
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Author : Daniel Gorenstein
language : en
Publisher:
Release Date :
The Classification Of Finite Simple Groups written by Daniel Gorenstein and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.