Group and Ring Theoretic Properties of Polycyclic Groups
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Beschreibung
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. They also touch on some aspects of topology, geometry and number theory. 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 not intended to be encyclopedic. Instead, it is 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 by any reader who has been exposed to some undergraduate algebra, especially groups, rings and vector spaces. Thus the book 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. The book then concludes with an extensive bibliography of items relating to polycyclic groups.
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.
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
Autor*in
B.A.F. Wehrfritz
Themen in »Group and Ring Theoretic Properties of Polycyclic Groups«
Group theory Noetherian rings Vector space algebra polycyclic groups ring theory
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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)()