The Classification Of The Finite Simple Groups Number 5

Author : Daniel Gorenstein
Publisher : American Mathematical Soc.
ISBN 13 : 9780821803912
Total Pages : 446 pages
Book Rating : 4.13/5 ( download)

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Download or read book The Classification of the Finite Simple Groups, Number 3 written by Daniel Gorenstein and published by American Mathematical Soc.. This book was released on 1994 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Inna Capdeboscq
Publisher : American Mathematical Society
ISBN 13 : 1470464373
Total Pages : 520 pages
Book Rating : 4.70/5 ( download)

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Download or read book The Classification of the Finite Simple Groups, Number 9 written by Inna Capdeboscq and published by American Mathematical Society. This book was released on 2021-02-22 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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 : Daniel Gorenstein
Publisher : Springer Science & Business Media
ISBN 13 : 1468484974
Total Pages : 339 pages
Book Rating : 4.77/5 ( download)

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Download or read book Finite Simple Groups written by Daniel Gorenstein and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Robert Wilson
Publisher : Springer Science & Business Media
ISBN 13 : 1848009879
Total Pages : 310 pages
Book Rating : 4.75/5 ( download)

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Download or read book The Finite Simple Groups written by Robert Wilson and published by Springer Science & Business Media. This book was released on 2009-12-14 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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].

Author : Daniel Gorenstein
Publisher : American Mathematical Soc.
ISBN 13 : 0821827774
Total Pages : 545 pages
Book Rating : 4.72/5 ( download)

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Download or read book The Classification of the Finite Simple Groups, Number 6 written by Daniel Gorenstein and published by American Mathematical Soc.. This book was released on 1994 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Daniel Gorenstein
Publisher : American Mathematical Soc.
ISBN 13 : 9780821827765
Total Pages : 488 pages
Book Rating : 4.66/5 ( 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 488 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 : 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 : Peter B. Kleidman
Publisher : Cambridge University Press
ISBN 13 : 052135949X
Total Pages : 317 pages
Book Rating : 4.98/5 ( download)

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Download or read book The Subgroup Structure of the Finite Classical Groups written by Peter B. Kleidman and published by Cambridge University Press. This book was released on 1990-04-26 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: With the classification of the finite simple groups complete, much work has gone into the study of maximal subgroups of almost simple groups. In this volume the authors investigate the maximal subgroups of the finite classical groups and present research into these groups as well as proving many new results. In particular, the authors develop a unified treatment of the theory of the 'geometric subgroups' of the classical groups, introduced by Aschbacher, and they answer the questions of maximality and conjugacy and obtain the precise shapes of these groups. Both authors are experts in the field and the book will be of considerable value not only to group theorists, but also to combinatorialists and geometers interested in these techniques and results. Graduate students will find it a very readable introduction to the topic and it will bring them to the very forefront of research in group theory.

Author : Manjul Bhargava
Publisher : American Mathematical Soc.
ISBN 13 : 1470436787
Total Pages : 229 pages
Book Rating : 4.80/5 ( download)

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Download or read book Finite Simple Groups: Thirty Years of the Atlas and Beyond written by Manjul Bhargava and published by American Mathematical Soc.. This book was released on 2017-07-24 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classification of Finite Simple Groups, one of the most monumental accomplishments of modern mathematics, was announced in 1983 with the proof completed in 2004. Since then, it has opened up a new and powerful strategy to approach and resolve many previously inaccessible problems in group theory, number theory, combinatorics, coding theory, algebraic geometry, and other areas of mathematics. This strategy crucially utilizes various information about finite simple groups, part of which is catalogued in the Atlas of Finite Groups (John H. Conway et al.), and in An Atlas of Brauer Characters (Christoph Jansen et al.). It is impossible to overestimate the roles of the Atlases and the related computer algebra systems in the everyday life of researchers in many areas of contemporary mathematics. The main objective of the conference was to discuss numerous applications of the Atlases and to explore recent developments and future directions of research, with focus on the interaction between computation and theory and applications to number theory and algebraic geometry. The papers in this volume are based on talks given at the conference. They present a comprehensive survey on current research in all of these fields.