Author: Guo Wenbing
Language: English
ISBN/ISSN: 7030074750
Published on: 2000-01
Hardcover
This book gives a systematic introduction to the theory of classes of groups,including research subjects,major(recent) research achievements, and directions for future research.It clearly and concisely treats a wealth of topics, such as a brief introduction to the fundamental knowledge of group theory;the classical part of the theory of classes of groups covering mainly F-covering subgroups,F-projectors ,F-iinjectors and F-normalisers; local formations;Schunck classes;Fitting classes;properties of local formations;formation constructions of finite groups and related applications; and the algebra of formations.
Audience
This volume will be of interest to mathematicians involved in group theory and generalisations ,algebras ,order,lattices,ordered algebraic structures,general mathematical systems and the mathematics of physics and chemistry.
Chapter I Fundamentals of the Theory of Finite Groups
11 Basic Concepts
12 Homomorphism Theorems
13 Primary Groups
14 Sylows Theorems
15 Automorphism Groups and Semidirect Products
16 The Jordan-Holder Theorem
17 Soluble Groups and TT-soluble Groups
18 Nilpotent Groups and TT-nilpotent Groups
19 Supersoluble Groups and TT-supersoluble Groups
110 Some Additional Information
Chapter 2 Classical -Subgroups
21 Operations on Classes of Finite Groups
22 -covering Subgroups, -projectors, -injectors
23 Theorems about Existence of -covering Subgroups and -projector
24 The conjugacy of -covering Subgroups
25 The Existence amd Conjugacy of -injectors
26 normalizers
27 Some Additional Information
Chapter 3 Formation Structures of Finite Groups
31 Methods of Constructing Local Formations
32 The Stability of Formations
33 On Complements of -coradicals
34 Minimal Non--groups
35 S-formations
36 Groups with Normalizers of Sylow Subgroups Belonging to a Given
Formation
37 Groups with Normalizers of Sylow Subgroups Complemented
38 Groups with Normalizers of Sylow Subgroups Having Given Indices
39 Groups with Given Local Subgroups
310 -subnormal Subgroups
Language: English
ISBN/ISSN: 7030074750
Published on: 2000-01
Hardcover
This book gives a systematic introduction to the theory of classes of groups,including research subjects,major(recent) research achievements, and directions for future research.It clearly and concisely treats a wealth of topics, such as a brief introduction to the fundamental knowledge of group theory;the classical part of the theory of classes of groups covering mainly F-covering subgroups,F-projectors ,F-iinjectors and F-normalisers; local formations;Schunck classes;Fitting classes;properties of local formations;formation constructions of finite groups and related applications; and the algebra of formations.
Audience
This volume will be of interest to mathematicians involved in group theory and generalisations ,algebras ,order,lattices,ordered algebraic structures,general mathematical systems and the mathematics of physics and chemistry.
Chapter I Fundamentals of the Theory of Finite Groups
11 Basic Concepts
12 Homomorphism Theorems
13 Primary Groups
14 Sylows Theorems
15 Automorphism Groups and Semidirect Products
16 The Jordan-Holder Theorem
17 Soluble Groups and TT-soluble Groups
18 Nilpotent Groups and TT-nilpotent Groups
19 Supersoluble Groups and TT-supersoluble Groups
110 Some Additional Information
Chapter 2 Classical -Subgroups
21 Operations on Classes of Finite Groups
22 -covering Subgroups, -projectors, -injectors
23 Theorems about Existence of -covering Subgroups and -projector
24 The conjugacy of -covering Subgroups
25 The Existence amd Conjugacy of -injectors
26 normalizers
27 Some Additional Information
Chapter 3 Formation Structures of Finite Groups
31 Methods of Constructing Local Formations
32 The Stability of Formations
33 On Complements of -coradicals
34 Minimal Non--groups
35 S-formations
36 Groups with Normalizers of Sylow Subgroups Belonging to a Given
Formation
37 Groups with Normalizers of Sylow Subgroups Complemented
38 Groups with Normalizers of Sylow Subgroups Having Given Indices
39 Groups with Given Local Subgroups
310 -subnormal Subgroups
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