Guo Wenbin's Books

The Theory of Classes of Groups

By: Guo Wenbin

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The Theory of Classes of Groups

By: Guo Wenbin

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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270

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Springer Science & Business Media

Published Date

ISBN 10

9401140545

ISBN 13

9789401140546

Structure Theory for Canonical Classes of Finite Groups

By: Wenbin Guo

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Structure Theory for Canonical Classes of Finite Groups

By: Wenbin Guo

This book offers a systematic introduction to recent achievements and development in research on the structure of finite non-simple groups, the theory of classes of groups and their applications. In particular, the related systematic theories are considered and some new approaches and research methods are described – e.g., the F-hypercenter of groups, X-permutable subgroups, subgroup functors, generalized supplementary subgroups, quasi-F-group, and F-cohypercenter for Fitting classes. At the end of each chapter, we provide relevant supplementary information and introduce readers to selected open problems.

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Page Count

369

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Springer

Published Date

ISBN 10

3662457474

ISBN 13

9783662457474

The Theory of Classes of Groups

By: Guo Wenbin

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The Theory of Classes of Groups

By: Guo Wenbin

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

270

Publisher

Springer Science & Business Media

Published Date

ISBN 10

9401140545

ISBN 13

9789401140546

Book's by Guo Wenbin

The Theory of Classes of Groups

The Theory of Classes of Groups

Structure Theory for Canonical Classes of Finite Groups

Structure Theory for Canonical Classes of Finite Groups

The Theory of Classes of Groups

The Theory of Classes of Groups

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