The Classification Of The Finite Simple Groups Part Iii Chapters 1 6 The Generic Case Stages 1 3a

Author : Daniel Gorenstein
Publisher :
ISBN 13 :
Total Pages : 490 pages
Book Rating : 4.77/5 ( download)

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Download or read book The Classification of the Finite Simple Groups: Part III, chapters 1-6: The generic case, stages 1-3a written by Daniel Gorenstein and published by . This book was released on 2002 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Daniel Gorenstein
Publisher : American Mathematical Soc.
ISBN 13 : 1470441896
Total Pages : 488 pages
Book Rating : 4.90/5 ( download)

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Download or read book The Classification of the Finite Simple Groups, Number 8: Part III, Chapters 12–17: The Generic Case, Completed written by Daniel Gorenstein and published by American Mathematical Soc.. This book was released on 2018-12-12 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Inna Capdeboscq
Publisher : American Mathematical Society
ISBN 13 : 1470475537
Total Pages : 587 pages
Book Rating : 4.36/5 ( download)

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Download or read book The Classification of the Finite Simple Groups, Number 10 written by Inna Capdeboscq and published by American Mathematical Society. This book was released on 2023-10-23 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Daniel Gorenstein
Publisher : American Mathematical Soc.
ISBN 13 : 0821827766
Total Pages : 482 pages
Book Rating : 4.65/5 ( download)

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Download or read book The Classification of the Finite Simple Groups, Number 5 written by Daniel Gorenstein and published by American Mathematical Soc.. This book was released on 1994 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Daniel Gorenstein
Publisher : American Mathematical Soc.
ISBN 13 : 082184069X
Total Pages : 344 pages
Book Rating : 4.96/5 ( download)

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Download or read book 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 published by American Mathematical Soc.. This book was released on 2018-02-15 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Michael Aschbacher
Publisher : American Mathematical Soc.
ISBN 13 : 0821853368
Total Pages : 362 pages
Book Rating : 4.68/5 ( download)

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Download or read book The Classification of Finite Simple Groups written by Michael Aschbacher and published by American Mathematical Soc.. This book was released on 2011 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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'.

Author : Michael Aschbacher
Publisher : American Mathematical Soc.
ISBN 13 : 082183410X
Total Pages : 496 pages
Book Rating : 4.07/5 ( download)

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Download or read book The Classification of Quasithin Groups written by Michael Aschbacher and published by American Mathematical Soc.. This book was released on 2004 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first of two volumes, this text offers results that are used in the proof of the main theoremthat lies behind quasithin groups, an class of finite simple groups. Some results are gathered from existing mathematical literature, but many are proven for the first time.

Author : Daniel Gorenstein
Publisher :
ISBN 13 :
Total Pages : 552 pages
Book Rating : 4.48/5 ( download)

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Download or read book The Classification of the Finite Simple Groups written by Daniel Gorenstein and published by . This book was released on 2005 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author :
Publisher :
ISBN 13 :
Total Pages : 840 pages
Book Rating : 4.38/5 ( download)

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Download or read book Journal of Lie Theory written by and published by . This book was released on 2006 with total page 840 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Daniel Gorenstein
Publisher :
ISBN 13 : 9780821827765
Total Pages : 467 pages
Book Rating : 4.66/5 ( download)

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Download or read book The Classification of the Finite Simple Groups written by Daniel Gorenstein and published by . This book was released on 2002 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: