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The Theory of Groups, Volume 1

Edition: 
2
Publisher: 
American Mathematical Society/Chelsea
Number of Pages: 
272
Price: 
26.00
ISBN: 
0-8284-0107-1
Date Received: 
Tuesday, February 1, 2005
Reviewable: 
Yes
Include In BLL Rating: 
Yes
Alexander G. Kurosh
Publication Date: 
1955
Format: 
Hardcover
Category: 
Textbook
BLL
06/15/2009
BLL Rating: 
Part One. The Elements of Group Theory

* Definition of a Group: 1.1 Algebraic operations; 1.2 Isomorphism. Homomorphism; 1.3 Groups; 1.4 Examples of groups
* Subgroups: 2.5 Subgroups; 2.6 Systems of generators. Cyclic groups; 2.7 Ascending sequences of groups
* Normal Subgroups: 3.8 Decomposition of a group with respect to a subgroup; 3.9 Normal subgroups; 3.10 The connection between normal subgroups, homomorphisms, and factor groups; 3.11 Classes of conjugate elements, and conjugate subgroups
* Endomorphisms and Automorphisms. Groups with Operators: 4.12 Endomorphisms and automorphisms; 4.13 The holomorph. Complete groups; 4.14 Characteristic and fully invariant subgroups; 4.15 Groups with operators
* Series of Subgroups. Direct Products. Defining Relations: 5.16 Normal series and composition series; 5.17 Direct products; 5.18 Free groups. Defining relations

Part Two. Abelian Groups

* Foundations of the theory of abelian groups; 6.19 The rank of an abelian group. Free abelian groups; 6.20 Finitely generated abelian groups; 6.21 The ring of endomorphisms of an abelian group; 6.22 Abelian groups with operators
* Primary and Mixed Abelian Groups: 7.23 Complete abelian groups; 7.24 Direct sums of cyclic groups; 7.25 Serving subgroups; 7.26 Primary groups without elements of infinite height; 7.27 Ulm factors. The existence theorem; 7.28 Ulm's theorem; 7.29 Mixed abelian groups
* Torsion-Free Abelian Groups: 8.30 Groups of rank 1. Types of elements of torsion-free groups; 8.31 Completely decomposable groups; 8.32 Other classes of abelian torsion-free groups

* Appendixes
* Bibliography
* Author Index
* Subject Index
Publish Book: 
Modify Date: 
Monday, June 15, 2009

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