Groups with Prescribed Quotient Groups and Associated Module Theory

Javier Otal, Igor Subbotin, Leonid Kurdochenko9789810247836, 981-02-4783-4

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 group problems. Evidently, this approach requires investigation of some specific types of modules: infinite simple modules and just infinite modules (note that every infinite noetherian module has either an infinite simple factor-module or a just infinite factor-module). This book will therefore be useful for group theorists as well as ring and module theorists. Also, the level, style, and presentation make the book easily accessible to graduate students.

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Table of contents :
Contents……Page 14
Preface……Page 8
Notation……Page 16
I Simple Modules……Page 18
1. On Annihilators of Modules……Page 20
2. The Structure of Simple Modules over Abelian Groups……Page 34
3. The Structure of Simple Modules over Some Generalizations of Abelian Groups……Page 42
4. Complements of Simple Submodules……Page 56
II Just Infinite Modules……Page 62
5. Some Results on Modules over Dedekind Domains……Page 64
6. Just Infinite Modules over FC-Hypercentral Groups……Page 78
7. Just Infinite Modules over Groups of Finite 0-Rank……Page 94
8. Just Infinite Modules over Polycyclic-by-Finite Groups……Page 108
9. Co-Layer-Finite Modules over Dedekind Domains……Page 118
III Just Non-X-Groups……Page 124
10. The Fitting Subgroup of Some Just Non-X-Groups……Page 126
11. Just Non-Abelain Groups……Page 132
12. Just Non-Hypercentral Groups and Just Non-Hypercentral Modules……Page 138
13. Groups with Many Nilpotent Factor-Groups……Page 148
14. Groups with Proper Periodic Factor-Groups……Page 160
15. Just Non-(Polycyclic-by-Finite) Groups……Page 172
16. Just Non-CC-Groups and Related Classes……Page 182
17. Groups Whose Proper Factor-Groups Have a Transitive Normality Relation……Page 198
Bibliography……Page 220
Author Index……Page 238
Subject Index……Page 242