| Document Type
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BL
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| Record Number
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850306
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| Main Entry
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Smith, Stephen D.,1948-
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| Title & Author
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Applying the classification of finite simple groups : : a user's guide /\ Stephen D. Smith.
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| Publication Statement
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Providence, Rhode Island :: American Mathematical Society,, [2018]
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| Series Statement
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Mathematical surveys and monographs ;; volume 230
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| Page. NO
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xiii, 231 pages ;; 27 cm
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| ISBN
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1470442914
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: 9781470442910
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| Bibliographies/Indexes
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Includes bibliographical references and index.
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| Contents
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Background : simple groups and their properties -- Outline of the proof of the CFSG : some main ideas -- Thompson factorization -- and its failure : FF-methods -- Recognition theorems for simple groups -- Representation theory of simple groups -- Maximal subgroups and primitive representations -- Geometries for simple groups -- Some fusion techniques for classification problems -- Some applications close to finite group theory -- Some applications farther afield from finite groups -- Appendix A. Some supplementary notes to the text -- Appendix B. Further remarks on certain exercises.
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| Abstract
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"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"--The publisher.
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| Subject
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Finite simple groups.
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| Subject
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Representations of groups.
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| Subject
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Finite simple groups.
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| Subject
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Group theory and generalizations-- Abstract finite groups-- Finite simple groups and their classification.
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| Subject
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Group theory and generalizations-- Connections with homological algebra and category theory-- Connections with homological algebra and category theory.
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Group theory and generalizations-- Linear algebraic groups and related topics-- Linear algebraic groups and related topics.
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Group theory and generalizations-- Permutation groups-- Permutation groups.
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Group theory and generalizations-- Representation theory of groups-- Representation theory of groups.
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Group theory and generalizations-- Research exposition (monographs, survey articles)
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Group theory and generalizations-- Structure and classification of infinite or finite groups-- Structure and classification of infinite or finite groups.
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| Subject
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Representations of groups.
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| Dewey Classification
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512/.2
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| LC Classification
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QA177.S645 2018
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| NLM classification
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20-0220D0520Bxx20Cxx20Exx20Gxx20Jxxmsc
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20Jxx.msc
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| Parallel Title
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Classification of finite simple groups
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