The Theory of Classes of Groups: 505 (Mathematics and Its Applications, 505) - Hardcover

Guo Wenbin

Hardcover

ISBN 10: 0792362683 ISBN 13: 9780792362685

Publisher: Springer, 2001

Synopsis

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.

About this title

Synopsis

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-injectors 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. 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.

Edition details

• Publisher: Springer
• Publication date: 2001
• Language: English
• ISBN 10: 0792362683
• ISBN 13: 9780792362685
• Binding: Hardcover
• Number of pages: 269