The Theory of Classes of Groups

The Theory of Classes of Groups
Author :
Publisher : Springer Science & Business Media
Total Pages : 270
Release :
ISBN-10 : 9789401140546
ISBN-13 : 9401140545
Rating : 4/5 (46 Downloads)

Book Synopsis The Theory of Classes of Groups by : Guo Wenbin

Download or read book The Theory of Classes of Groups written by Guo Wenbin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


The Theory of Classes of Groups Related Books

The Theory of Classes of Groups
Language: en
Pages: 270
Authors: Guo Wenbin
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

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 in
Structure Theory for Canonical Classes of Finite Groups
Language: en
Pages: 369
Authors: Wenbin Guo
Categories: Mathematics
Type: BOOK - Published: 2015-04-23 - Publisher: Springer

DOWNLOAD EBOOK

This book offers a systematic introduction to recent achievements and development in research on the structure of finite non-simple groups, the theory of classe
The Theory of Classes of Groups
Language: en
Pages: 276
Authors: Guo Wenbin
Categories: Mathematics
Type: BOOK - Published: 2000 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

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 in
A Course in the Theory of Groups
Language: en
Pages: 498
Authors: Derek J.S. Robinson
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

" A group is defined by means of the laws of combinations of its symbols," according to a celebrated dictum of Cayley. And this is probably still as good a one-
A Course in Finite Group Representation Theory
Language: en
Pages: 339
Authors: Peter Webb
Categories: Mathematics
Type: BOOK - Published: 2016-08-19 - Publisher: Cambridge University Press

DOWNLOAD EBOOK

This graduate-level text provides a thorough grounding in the representation theory of finite groups over fields and rings. The book provides a balanced and com