The Theory of Classes of Groups

1. Front Matter

   Pages i-xi

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2. Fundamentals of the Theory of Finite Groups

   • Guo Wenbin

   Pages 1-57

3. Classical F-Subgroups

   • Guo Wenbin

   Pages 58-95

4. Formation Structures of Finite Groups

   • Guo Wenbin

   Pages 96-166

5. Algebra of Formations

   • Guo Wenbin

   Pages 167-224

6. Supplementary Information on Algebra and Theory of Sets

   • Guo Wenbin

   Pages 225-236

7. Back Matter

   Pages 237-258

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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.

• Algebraic structure
• Group theory
• Lattice
• Mathematica
• algebra
• finite group

• Mathematics Department, Science College, Yangzhou University, Yangzhou, P. R. China

  Guo Wenbin

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