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Simple Groups Of Finite Morley Rank
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Book Synopsis Simple Groups of Finite Morley Rank by : Tuna Altınel
Download or read book Simple Groups of Finite Morley Rank written by Tuna Altınel and published by American Mathematical Soc.. This book was released on 2008 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book gives a detailed presentation of the classification of the simple groups of finite Morley rank which contain a nontrivial unipotent 2-subgroup. They are linear algebraic groups over algebraically closed fields of characteristic 2. Although the story told in the book is inspired by the classification of the finite simple groups, it goes well beyond this source of inspiration. Not only do the techniques adapted from finite group theory cover, in a peculiar way, various portions of the three generations of approaches to finite simple groups but model theoretic methods also play an unexpected role. The book contains a complete account of all this material, part of which has not been published. In addition, almost every general result about groups of finite Morley rank is exposed in detail and the book ends with a chapter where the authors provide a list of open problems in the relevant fields of mathematics. As a result, the book provides food for thought to finite group theorists, model theorists, and algebraic geometers who are interested in group theoretic problems.
Book Synopsis Simple Groups of Finite Morley Rank of Odd and Degenerate Type by : Jeffrey Burdges
Download or read book Simple Groups of Finite Morley Rank of Odd and Degenerate Type written by Jeffrey Burdges and published by . This book was released on 2004 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Classification of the Finite Simple Groups by : Daniel Gorenstein
Download or read book The Classification of the Finite Simple Groups written by Daniel Gorenstein and published by American Mathematical Soc.. This book was released on 1994-11-18 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Finite and Locally Finite Groups by : B. Hartley
Download or read book Finite and Locally Finite Groups written by B. Hartley and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Handbook of Algebra by : M. Hazewinkel
Download or read book Handbook of Algebra written by M. Hazewinkel and published by Elsevier. This book was released on 2000-04-06 with total page 899 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Algebra
Book Synopsis Finite Simple Groups by : Daniel Gorenstein
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.
Book Synopsis Groups of Finite Morley Rank by : Alexandre Borovik
Download or read book Groups of Finite Morley Rank written by Alexandre Borovik and published by OUP Oxford. This book was released on 1994 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to the theory of groups of finite Morley rank. These groups arise in model theory and generalize the concept of algebraic groups over algebraically closed fields. The book contains almost all the known results in the subject. Trying to attract pure group theorists in thesubject and to prepare the graduate student to start the research in the area, the authors adopted an algebraic and self evident point of view rather than a model theoretic one, and developed the theory from scratch. All the necessary model theoretical and group theoretical notions are explained inlength. The book is full of exercises and examples and one of its chapters contains a discussion of open problems and a program for further research.
Book Synopsis The Classification of the Finite Simple Groups, Number 10 by : Inna Capdeboscq
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.
Book Synopsis Groups of Finite Morley Rank with Strongly Embedded Subgroups by : Tuna Altınel
Download or read book Groups of Finite Morley Rank with Strongly Embedded Subgroups written by Tuna Altınel and published by . This book was released on 1994 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Algebraic Groups and their Representations by : R.W. Carter
Download or read book Algebraic Groups and their Representations written by R.W. Carter and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains 19 articles written by speakers at the Advanced Study Institute on 'Modular representations and subgroup structure of al gebraic groups and related finite groups' held at the Isaac Newton Institute, Cambridge from 23rd June to 4th July 1997. We acknowledge with gratitude the financial support given by the NATO Science Committee to enable this ASI to take place. Generous financial support was also provided by the European Union. We are also pleased to acknowledge funds given by EPSRC to the Newton Institute which were used to support the meeting. It is a pleasure to thank the Director of the Isaac Newton Institute, Professor Keith Moffatt, and the staff of the Institute for their dedicated work which did so much to further the success of the meeting. The editors wish to thank Dr. Ross Lawther and Dr. Nick Inglis most warmly for their help in the production of this volume. Dr. Lawther in particular made an invaluable contribution in preparing the volume for submission to the publishers. Finally we wish to thank the distinguished speakers at the ASI who agreed to write articles for this volume based on their lectures at the meet ing. We hope that the volume will stimulate further significant advances in the theory of algebraic groups.
Book Synopsis The Classification of Finite Simple Groups by : Daniel Gorenstein
Download or read book The Classification of Finite Simple Groups written by Daniel Gorenstein and published by Springer Science & Business Media. This book was released on 2013-11-22 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Finite Simple Groups by : Robert Wilson
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].
Book Synopsis Groups, Combinatorics and Geometry by : Martin W. Liebeck
Download or read book Groups, Combinatorics and Geometry written by Martin W. Liebeck and published by Cambridge University Press. This book was released on 1992-09-10 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a collection of papers on the subject of the classification of finite simple groups.
Book Synopsis Logic Colloquium 2005 by : Costas Dimitracopoulos
Download or read book Logic Colloquium 2005 written by Costas Dimitracopoulos and published by Cambridge University Press. This book was released on 2008 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Annual European Meeting of the Association for Symbolic Logic, generally known as the Logic Colloquium, is the most prestigious annual meeting in the field. Many of the papers presented there are invited surveys of developments, and the rest of the papers are chosen to complement the invited talks. This 2007 volume includes surveys, tutorials, and selected research papers from the 2005 meeting. Highlights include three papers on different aspects of connections between model theory and algebra; a survey of major advances in combinatorial set theory; a tutorial on proof theory and modal logic; and a description of Bernay's philosophy of mathematics.
Book Synopsis Tits Buildings and the Model Theory of Groups by : Katrin Tent
Download or read book Tits Buildings and the Model Theory of Groups written by Katrin Tent and published by Cambridge University Press. This book was released on 2002-01-03 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to buildings and their geometries with emphasis on model theoretic constructions, covering recent developments.
Download or read book Logic and Algebra written by Yi Zhang and published by American Mathematical Soc.. This book was released on 2002 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume outlines current developments in model theory and combinatorial set theory and presents state-of-the-art research. Well-known researchers report on their work in model theory and set theory with applications to algebra. The papers of J. Brendle and A. Blass present one of the most interesting areas of set theory. Brendle gives a very detailed and readable account of Shelah's solution for the long-standing problem of $\mathrm{Con (\mathfrak{d a )$. It could be used in anadvanced graduate seminar on set theory. Papers by T. Altinel, J. T. Baldwin, R. Grossberg, W. Hodges, T. Hyttinen, O. Lessmann, and B. Zilber deal with questions of model theory from the viewpoint of stability theory. Here, Zilber constructs an $\omega$-stable complete theory of ``pseudo-analytic''structures on algebraically closed fields. This result is part of his program of the model-theoretic study of analytic structures by including Hrushovski's method in the analytic context. The book presents this and further developments in model theory. It is geared toward advanced graduate students and researchers interested in logic and foundations, algebra, and algebraic geometry.
Download or read book Stable Groups written by Bruno Poizat and published by American Mathematical Soc.. This book was released on 2001 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the English translation of the book originally published in 1987. It is a faithful reproduction of the original, supplemented by a new Foreword and brought up to date by a short postscript. The book gives an introduction by a specialist in contemporary mathematical logic to the model-theoretic study of groups, i.e., into what can be said about groups, and for that matter, about all the traditional algebraic objects. The author introduces the groups of finite Morley rank (those satisfying the most restrictive assumptions from the point of view of logic), and highlights their resemblance to algebraic groups, of which they are the prototypes. (All the necessary prerequisites from algebraic geometry are included in the book.) Then, whenever possible, generalizations of properties of groups of finite Morley type to broader classes of superstables and stable groups are described. The exposition in the first four chapters can be understood by mathematicians who have some knowledge of logic (model theory). The last three chapters are intended for specialists in mathematical logic.
