Overview
- A short and concise treatment of the essential results with proofs that are clear and easy to follow. This book will prepare readers for research in related areas.
- Accessible to researchers working in areas other than group theory who find themselves involved with polycyclic groups; no previous knowledge of polycyclic groups is assumed.
- Introduces all the various techniques used in the proof of Roseblade's residual finiteness theorem.
- Written by a renowned expert in the field of infinite groups.
- Includes supplementary material: sn.pub/extras
Part of the book series: Algebra and Applications (AA, volume 10)
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Table of contents (10 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
Reviews
From the reviews:
“The book under review consists of 10 chapters and is devoted to the systematic study of polycyclic groups from the beginning in the late 1930’s up to now. … The book is written clearly, with a high scientific level. … It is quite accessible to research workers not only in the area of group theory, but also in other areas, who find themselves, involved with polycyclic groups. The Bibliography is rich and reflects the development of the theory from very early time up to now.” (Bui Xuan Hai, Zentralblatt MATH, Vol. 1206, 2011)Authors and Affiliations
Bibliographic Information
Book Title: Group and Ring Theoretic Properties of Polycyclic Groups
Authors: B.A.F. Wehrfritz
Series Title: Algebra and Applications
DOI: https://doi.org/10.1007/978-1-84882-941-1
Publisher: Springer London
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag London 2009
Hardcover ISBN: 978-1-84882-940-4Published: 15 December 2009
Softcover ISBN: 978-1-4471-2530-3Published: 01 March 2012
eBook ISBN: 978-1-84882-941-1Published: 28 November 2009
Series ISSN: 1572-5553
Series E-ISSN: 2192-2950
Edition Number: 1
Number of Pages: VIII, 128
Topics: Group Theory and Generalizations, Associative Rings and Algebras, Commutative Rings and Algebras