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The Theory of Classes of Groups (Paperback, Softcover reprint of the original 1st ed. 2000)
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The Theory of Classes of Groups (Paperback, Softcover reprint of the original 1st ed. 2000)
Series: Mathematics and Its Applications, 505
Expected to ship within 10 - 15 working days
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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.
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