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|a 9789401140546
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|a 10.1007/978-94-011-4054-6
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|a (DE-He213)978-94-011-4054-6
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|a Guo Wenbin.
|e author.
|4 aut
|4 http://id.loc.gov/vocabulary/relators/aut
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|a The Theory of Classes of Groups
|h [electronic resource] /
|c by Guo Wenbin.
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| 250 |
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|a 1st ed. 2000.
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| 264 |
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|a Dordrecht :
|b Springer Netherlands :
|b Imprint: Springer,
|c 2000.
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| 300 |
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|a XI, 258 p.
|b online resource.
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|a text
|b txt
|2 rdacontent
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|a computer
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|2 rdamedia
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|a online resource
|b cr
|2 rdacarrier
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| 347 |
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|a text file
|b PDF
|2 rda
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| 490 |
1 |
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|a Mathematics and Its Applications ;
|v 505
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| 490 |
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|a Springer eBook Collection
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|a 1 Fundamentals of the Theory of Finite Groups -- §1.1 Basic Concepts -- §1.2 Homomorphism Theorems -- §1.3 Primary Groups -- §1.4 Sylow’s Theorems -- §1.5 Automorphism Groups and Semidirect Products -- §1.6 The Jordan-Hölder Theorem -- §1.7 Soluble Groups and ?-soluble Groups -- §1.8 Nilpotent Groups and ?-nilpotent Groups -- §1.9 Supersoluble Groups and ?-supersoluble Groups -- §1.10 Some Additional Information -- 2 Classical F-Subgroups -- §2.1 Operations on Classes of Finite Groups -- §2.2 X-covering Subgroups, X-projectors, X-injectors -- §2.3 Theorems about Existence of F-covering Subgroups and F-projectors -- §2.4 The conjugacy of F-covering Subgroups -- §2.5 The Existence amd Conjugacy of F-injectors -- §2.6 .F-normalizers -- §2.7 Some Additional Information -- 3 Formation Structures of Finite Groups -- §3.1 Methods of Constructing Local Formations -- §3.2 The Stability of Formations -- §3.3 On Complements of F-coradicals -- §3.4 Minimal Non-F-groups -- §3.5 Š-formations -- §3.6 Groups with Normalizers of Sylow Subgroups Belonging to a Given Formation -- §3.7 Groups with Normalizers of Sylow Subgroups Complemented -- §3.8 Groups with Normalizers of Sylow Subgroups Having Given Indices -- §3.9 Groups with Given Local Subgroups -- §3.10 F-subnormal Subgroups -- §3.11 Some Additional Information -- 4 Algebra of Formations -- §4.1 Free Groups and Varieties of Groups -- §4.2 Generated Formations -- §4.3 Critical Formations -- §4.4 Local Formations with Complemented Subformations -- §4.5 Some Additional Information -- 5 Supplementary Information on Algebra and Theory of Sets -- §5.1 Partially Ordered Sets and Lattices -- §5.2 Classical Algebras -- §5.3 Modules over Algebras -- Index of Subjects -- List of Symbols.
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|a 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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|a Loaded electronically.
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| 590 |
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|a Electronic access restricted to members of the Holy Cross Community.
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| 650 |
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|a Group theory.
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| 650 |
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|a Nonassociative rings.
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| 650 |
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|a Rings (Algebra).
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| 650 |
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|a Algebra.
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| 650 |
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|a Ordered algebraic structures.
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| 650 |
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|a Mathematical logic.
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| 650 |
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|a Applied mathematics.
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| 650 |
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|a Engineering mathematics.
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| 650 |
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|a Chemometrics.
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| 690 |
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|a Electronic resources (E-books)
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| 710 |
2 |
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|a SpringerLink (Online service)
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| 773 |
0 |
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|t Springer eBooks
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| 830 |
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|a Mathematics and Its Applications ;
|v 505
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| 830 |
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|a Springer eBook Collection.
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| 856 |
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|u https://holycross.idm.oclc.org/login?auth=cas&url=https://doi.org/10.1007/978-94-011-4054-6
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