Algebra and Applications

Group and Ring Theoretic Properties of Polycyclic Groups

Authors: Wehrfritz, Bertram

  • Offers 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
  • 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
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eBook $89.00
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  • ISBN 978-1-84882-941-1
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Hardcover $119.00
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  • ISBN 978-1-84882-940-4
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Softcover $119.00
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  • ISBN 978-1-4471-2530-3
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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. 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.

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)

Table of contents (10 chapters)

  • Some Basic Group Theory

    Wehrfritz, B. A. F.

    Pages 1-11

  • The Basic Theory of Polycyclic Groups

    Wehrfritz, B. A. F.

    Pages 13-28

  • Some Ring Theory

    Wehrfritz, B. A. F.

    Pages 29-39

  • Soluble Linear Groups

    Wehrfritz, B. A. F.

    Pages 41-54

  • Further Group-Theoretic Properties of Polycyclic Groups

    Wehrfritz, B. A. F.

    Pages 55-62

Buy this book

eBook $89.00
price for USA (gross)
  • ISBN 978-1-84882-941-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $119.00
price for USA
  • ISBN 978-1-84882-940-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $119.00
price for USA
  • ISBN 978-1-4471-2530-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Group and Ring Theoretic Properties of Polycyclic Groups
Authors
Series Title
Algebra and Applications
Series Volume
10
Copyright
2009
Publisher
Springer-Verlag London
Copyright Holder
Springer-Verlag London
eBook ISBN
978-1-84882-941-1
DOI
10.1007/978-1-84882-941-1
Hardcover ISBN
978-1-84882-940-4
Softcover ISBN
978-1-4471-2530-3
Series ISSN
1572-5553
Edition Number
1
Number of Pages
VIII, 128
Topics