Groups with prescribed quotient groups and associated module theory / L. Kurdachenko, J. Otal, I. Subbotin.

Format:

Book

Author/Creator:

Kurdachenko, Leonid A., 1949-

Contributor:

Otal, Jean-Pierre.

Subbotin, Igor Ya., 1950-

Series:

Series in algebra ; v. 8.

Series in algebra ; v. 8

Language:

English

Subjects (All):

Group theory.

Modules (Algebra).

Physical Description:

1 online resource (244 p.)

Edition:

1st ed.

Place of Publication:

River Edge, NJ : World Scientific, c2002.

Language Note:

English

Summary:

The influence of different gomomorphic images on the structure of a group is one of the most important and natural problems of group theory. The problem of describing a group with all its gomomorphic images known, i.e. reconstructing the whole thing using its reflections, seems especially natural and promising. This theme has a history that is almost a half-century long. The authors of this book present well-established results as well as newer, contemporary achievements in this area from the common integral point of view. This view is based on the implementation of module theory for solving

Contents:

Contents ; Preface ; Notation ; I Simple Modules ; 1. On Annihilators of Modules ; 2. The Structure of Simple Modules over Abelian Groups ; 3. The Structure of Simple Modules over Some Generalizations of Abelian Groups ; 4. Complements of Simple Submodules ; II Just Infinite Modules

5. Some Results on Modules over Dedekind Domains 6. Just Infinite Modules over FC-Hypercentral Groups ; 7. Just Infinite Modules over Groups of Finite 0-Rank ; 8. Just Infinite Modules over Polycyclic-by-Finite Groups ; 9. Co-Layer-Finite Modules over Dedekind Domains

III Just Non-X-Groups 10. The Fitting Subgroup of Some Just Non-X-Groups ; 11. Just Non-Abelain Groups ; 12. Just Non-Hypercentral Groups and Just Non-Hypercentral Modules ; 13. Groups with Many Nilpotent Factor-Groups ; 14. Groups with Proper Periodic Factor-Groups

15. Just Non-(Polycyclic-by-Finite) Groups 16. Just Non-CC-Groups and Related Classes ; 17. Groups Whose Proper Factor-Groups Have a Transitive Normality Relation ; Bibliography ; Author Index ; Subject Index

Notes:

Description based upon print version of record.

Includes bibliographical references (p. 203-219) and index.

ISBN:

9789812778291

9812778292

OCLC:

879023570