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Author: Gregory Karpilovsky
Publisher: Oxford University Press, USA
ISBN:
Category : Mathematics
Languages : en
Pages : 322
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Book Description
During the last thirty years, much research has been devoted to the study of various properties of the second cohomology group, also known as the Schur multiplier. Clear and carefully developed, this book conveys a comprehensive picture of the current state of this subject and offers a unified treatment of a wealth of important results. It also provides a wide range of skill-sharpening mathematical techniques which will prove useful to graduate students and researchers in algebra.
Author: Gregory Karpilovsky
Publisher: Oxford University Press, USA
ISBN:
Category : Mathematics
Languages : en
Pages : 322
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Book Description
During the last thirty years, much research has been devoted to the study of various properties of the second cohomology group, also known as the Schur multiplier. Clear and carefully developed, this book conveys a comprehensive picture of the current state of this subject and offers a unified treatment of a wealth of important results. It also provides a wide range of skill-sharpening mathematical techniques which will prove useful to graduate students and researchers in algebra.
Author: Michael Aschbacher
Publisher: American Mathematical Soc.
ISBN: 0821853368
Category : Mathematics
Languages : en
Pages : 362
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Book Description
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: 1468484974
Category : Mathematics
Languages : en
Pages : 339
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Book Description
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: Stephen D. Smith
Publisher: American Mathematical Soc.
ISBN: 1470442914
Category : Mathematics
Languages : en
Pages : 248
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Book Description
Classification of Finite Simple Groups (CFSG) is a major project involving work by hundreds of researchers. The work was largely completed by about 1983, although final publication of the “quasithin” part was delayed until 2004. Since the 1980s, CFSG has had a huge influence on work in finite group theory and in many adjacent fields of mathematics. This book attempts to survey and sample a number of such topics from the very large and increasingly active research area of applications of CFSG. The book is based on the author's lectures at the September 2015 Venice Summer School on Finite Groups. With about 50 exercises from original lectures, it can serve as a second-year graduate course for students who have had first-year graduate algebra. It may be of particular interest to students looking for a dissertation topic around group theory. It can also be useful as an introduction and basic reference; in addition, it indicates fuller citations to the appropriate literature for readers who wish to go on to more detailed sources.
Author: F. R. Beyl
Publisher: Springer
ISBN: 3540395423
Category : Mathematics
Languages : en
Pages : 283
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Book Description
Author: Robert L. Jr. Griess
Publisher: Springer Science & Business Media
ISBN: 9783540627784
Category : Mathematics
Languages : en
Pages : 184
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Book Description
The 20 sporadics involved in the Monster, the largest sporadic group, constitute the Happy Family. This book is a leisurely and rigorous study of two of their three generations. The level is suitable for graduate students with little background in general finite group theory, established mathematicians and mathematical physicists.
Author: Robert L. Jr. Griess
Publisher: Springer Science & Business Media
ISBN: 3662035162
Category : Mathematics
Languages : en
Pages : 175
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Book Description
The 20 sporadics involved in the Monster, the largest sporadic group, constitute the Happy Family. This book is a leisurely and rigorous study of two of their three generations. The level is suitable for graduate students with little background in general finite group theory, established mathematicians and mathematical physicists.
Author: Daniel Gorenstein
Publisher: American Mathematical Soc.
ISBN: 0821822764
Category : Mathematics
Languages : en
Pages : 743
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Book Description
Studies the generic finite simple group of characteristic 2 type whose proper subgroups are of known type. The authors' principal result (the Trichotomy Theorem) asserts that such a group has one of three precisely determined internal structures.
Author: Bruce Cooperstein
Publisher: American Mathematical Soc.
ISBN: 0821814400
Category : Mathematics
Languages : en
Pages : 654
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Book Description
Author: B. Hartley
Publisher: Springer Science & Business Media
ISBN: 9401103291
Category : Mathematics
Languages : en
Pages : 469
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Book Description
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
