Groups with Prescribed Quotient Groups and Associated Module Theory

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...
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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.
Contents: "Simple Modules: "On Annihilators of ModulesThe Structure of Simple Modules Over Abelian GroupsThe Structure of Simple Modules Over Some Generalization of Abelian GroupsComplements of Simple Submodules"Just Infinite Modules: "Some Results on Modules Over Dedekind DomainsJust Infinite Modules Over "FC"-Hypercentral GroupsJust Infinite Modules Over Groups of Finite 0-RankJust Infinite Modules Over Polycyclic-By-Finite GroupsCo-Layer-Finite Modules Over a Dedekind Domains"Just Non-X-Groups: "The Fitting Subgroup of Some Just Non-X-GroupsJust Non-Abelian GroupsJust Non-Hypercentral Groups and Just Non-Hypercentral ModulesGroups with Many Nilpotent Factor-GroupsGroups with Proper Periodic Factor-GroupsJust Non-(Polycyclic-By-Finite) GroupsJust Non-"CC"-Groups and Related ClassesGroups Whose Proper Factor-Groups Have a Transitive Normality Relation
Readership: Researchers, academics and graduate students in algebra and number theory.