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" The Theory of Classes of Groups "
by Guo Wenbin.
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BL
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| Record Number
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579599
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b408818
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| Main Entry
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Wenbin, Guo.
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| Title & Author
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The Theory of Classes of Groups\ by Guo Wenbin.
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| Publication Statement
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Dordrecht :: Springer Netherlands :: Imprint: Springer,, 2000.
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| Series Statement
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Mathematics and Its Applications ;; 505
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| ISBN
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9789401140546
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: 9789401057851
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| Contents
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1 Fundamentals of the Theory of Finite Groups -- {sect}1.1 Basic Concepts -- {sect}1.2 Homomorphism Theorems -- {sect}1.3 Primary Groups -- {sect}1.4 Sylow's Theorems -- {sect}1.5 Automorphism Groups and Semidirect Products -- {sect}1.6 The Jordan-Hölder Theorem -- {sect}1.7 Soluble Groups and ?-soluble Groups -- {sect}1.8 Nilpotent Groups and ?-nilpotent Groups -- {sect}1.9 Supersoluble Groups and ?-supersoluble Groups -- {sect}1.10 Some Additional Information -- 2 Classical F-Subgroups -- {sect}2.1 Operations on Classes of Finite Groups -- {sect}2.2 X-covering Subgroups, X-projectors, X-injectors -- {sect}2.3 Theorems about Existence of F-covering Subgroups and F-projectors -- {sect}2.4 The conjugacy of F-covering Subgroups -- {sect}2.5 The Existence amd Conjugacy of F-injectors -- {sect}2.6 .F-normalizers -- {sect}2.7 Some Additional Information -- 3 Formation Structures of Finite Groups -- {sect}3.1 Methods of Constructing Local Formations -- {sect}3.2 The Stability of Formations -- {sect}3.3 On Complements of F-coradicals -- {sect}3.4 Minimal Non-F-groups -- {sect}3.5 Š-formations -- {sect}3.6 Groups with Normalizers of Sylow Subgroups Belonging to a Given Formation -- {sect}3.7 Groups with Normalizers of Sylow Subgroups Complemented -- {sect}3.8 Groups with Normalizers of Sylow Subgroups Having Given Indices -- {sect}3.9 Groups with Given Local Subgroups -- {sect}3.10 F-subnormal Subgroups -- {sect}3.11 Some Additional Information -- 4 Algebra of Formations -- {sect}4.1 Free Groups and Varieties of Groups -- {sect}4.2 Generated Formations -- {sect}4.3 Critical Formations -- {sect}4.4 Local Formations with Complemented Subformations -- {sect}4.5 Some Additional Information -- 5 Supplementary Information on Algebra and Theory of Sets -- {sect}5.1 Partially Ordered Sets and Lattices -- {sect}5.2 Classical Algebras -- {sect}5.3 Modules over Algebras -- Index of Subjects -- List of Symbols.
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| Abstract
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One of the characteristics of modern algebra is the development of new tools and concepts for exploring classes of algebraic systems, whereas the research on individual algebraic systems (e. g. , groups, rings, Lie algebras, etc. ) continues along traditional lines. The early work on classes of alge bras was concerned with showing that one class X of algebraic systems is actually contained in another class F. Modern research into the theory of classes was initiated in the 1930's by Birkhoff's work [1] on general varieties of algebras, and Neumann's work [1] on varieties of groups. A. I. Mal'cev made fundamental contributions to this modern development. ln his re ports [1, 3] of 1963 and 1966 to The Fourth All-Union Mathematics Con ference and to another international mathematics congress, striking the ories of classes of algebraic systems were presented. These were later included in his book [5]. International interest in the theory of formations of finite groups was aroused, and rapidly heated up, during this time, thanks to the work of Gaschiitz [8] in 1963, and the work of Carter and Hawkes [1] in 1967. The major topics considered were saturated formations, Fitting classes, and Schunck classes. A class of groups is called a formation if it is closed with respect to homomorphic images and subdirect products. A formation is called saturated provided that G E F whenever Gjip(G) E F.
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Mathematics.
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Chemistry-- Mathematics.
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Group theory.
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Algebra.
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Logic, Symbolic and mathematical.
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| Added Entry
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SpringerLink (Online service)
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