1.

Record Nr.

UNINA9910819221003321

Autore

Kurdachenko L

Titolo

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

Pubbl/distr/stampa

River Edge, NJ, : World Scientific, c2002

ISBN

981-277-829-2

Edizione

[1st ed.]

Descrizione fisica

1 online resource (244 p.)

Collana

Series in algebra ; ; v. 8

Altri autori (Persone)

OtalJean-Pierre

SubbotinIgor Ya. <1950->

Disciplina

512/.2

Soggetti

Group theory

Modules (Algebra)

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Description based upon print version of record.

Nota di bibliografia

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

Nota di contenuto

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

Sommario/riassunto

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