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Mathematics and Its Applications

The Theory of Classes of Groups

Authors: Guo Wenbin

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About this book

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.

Table of contents (5 chapters)

Table of contents (5 chapters)

Buy this book

eBook $64.99
price for USA in USD
  • ISBN 978-94-011-4054-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.99
price for USA in USD
Softcover $84.99
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
The Theory of Classes of Groups
Authors
Series Title
Mathematics and Its Applications
Series Volume
505
Copyright
2000
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media Dordrecht
Distribution Rights
No sales rights in People's Republic of China
eBook ISBN
978-94-011-4054-6
DOI
10.1007/978-94-011-4054-6
Hardcover ISBN
978-0-7923-6268-5
Softcover ISBN
978-94-010-5785-1
Edition Number
1
Number of Pages
XI, 258
Topics

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