Groups with prescribed quotient groups and associated module theory

著者

• Kurdachenko, L.
• Otal, J.
• Subbotin, I.

書誌事項

Groups with prescribed quotient groups and associated module theory

L. Kurdachenko, J. Otal, I. Subbotin

（Series in algebra, vol. 8）

World Scientific, c2002

注記

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

内容説明・目次

内容説明

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.

目次

• Simple Modules: On Annihilators of Modules
• The Structure of Simple Modules Over Abelian Groups
• The Structure of Simple Modules Over Some Generalization of Abelian Groups
• Complements of Simple Submodules
• Just Infinite Modules: Some Results on Modules Over Dedekind Domains
• Just Infinite Modules Over FC-Hypercentral Groups
• Just Infinite Modules Over Groups of Finite 0-Rank
• Just Infinite Modules Over Polycyclic-By-Finite Groups
• Co-Layer-Finite Modules Over a Dedekind Domains
• Just Non-X-Groups: The Fitting Subgroup of Some Just Non-X-Groups
• Just Non-Abelian Groups
• Just Non-Hypercentral Groups and Just Non-Hypercentral Modules
• Groups with Many Nilpotent Factor-Groups
• Groups with Proper Periodic Factor-Groups
• Just Non-(Polycyclic-By-Finite) Groups
• Just Non-CC-Groups and Related Classes
• Groups Whose Proper Factor-Groups Have a Transitive Normality Relation.

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詳細情報

• NII書誌ID(NCID): BA5586149X
• ISBN:
  • 9810247834
• 出版国コード: si
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Singapore
• ページ数/冊数: xvi, 227 p.
• 大きさ: 23 cm
• 親書誌ID:
  • BA21239867