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Main Data
Author: Bertram Wehrfritz
Title: Group and Ring Theoretic Properties of Polycyclic Groups
Publisher: Springer-Verlag
ISBN/ISSN: 9781848829411
Edition: 1
Price: CHF 82.50
Publication date: 01/01/2009
Content
Category: Wirtschaft/Management
Language: English
Technical Data
Pages: 128
Kopierschutz: DRM
Geräte: PC/MAC/eReader/Tablet
Formate: PDF
Table of contents

Polycyclic groups are built from cyclic groups in a specific way. They arise in many contexts within group theory itself but also more generally in algebra, for example in the theory of Noetherian rings. The first half of this book develops the standard group theoretic techniques for studying polycyclic groups and the basic properties of these groups. The second half then focuses specifically on the ring theoretic properties of polycyclic groups and their applications, often to purely group theoretic situations.

The book is intended to be a study manual for graduate students and researchers coming into contact with polycyclic groups, where the main lines of the subject can be learned from scratch. Thus it has been kept short and readable with a view that it can be read and worked through from cover to cover. At the end of each topic covered there is a description without proofs, but with full references, of further developments in the area. An extensive bibliography then concludes the book.

Table of contents
Preface6
Contents8
1 Some Basic Group Theory9
2 The Basic Theory of Polycyclic Groups20
3 Some Ring Theory36
4 Soluble Linear Groups47
5 Further Group-Theoretic Properties of Polycyclic Groups61
6 Hypercentral Groups and Rings69
7 Groups Acting on Finitely Generated Commutative Rings81
8 Prime Ideals in Polycyclic Group Rings94
9 The Structure of Modules over Polycyclic Groups104
10 Semilinear and Skew Linear Groups113
Notation121
Bibliography124
Index129