SpringerBriefs in Mathematics

Lectures on Finitely Generated Solvable Groups

Authors: Bencsath, K.A., Bonanome, M.C., Dean, M.H., Zyman, M.

  • ​​​​​​Includes a foreword by Gilbert Baumslag, a world renowned expert in combinatorial group theory
  • Serves as a field guide to the class of finitely generated solvable groups from a combinatorial group theory perspective
  • Provides examples to help illustrate key concepts 
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  • ISBN 978-1-4614-5449-6
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About this book

Lectures on Finitely Generated Solvable Groups are based on the “Topics in Group Theory" course focused on finitely generated solvable groups that was given by Gilbert G. Baumslag at the Graduate School and University Center of the City University of New York.  While knowledge about finitely generated nilpotent groups is extensive, much less is known about the more general class of solvable groups containing them.  The study of finitely generated solvable groups involves many different threads; therefore these notes contain discussions on HNN extensions; amalgamated and wreath products; and other concepts from combinatorial group theory as well as commutative algebra.  Along with Baumslag’s Embedding Theorem for Finitely Generated Metabelian Groups, two theorems of Bieri and Strebel are presented to provide a solid foundation for understanding the fascinating class of finitely generated solvable groups.  Examples are also supplied, which help illuminate many of the key concepts contained in the notes.  Requiring only a modest initial group theory background from graduate and post-graduate students, these notes provide a field guide to the class of finitely generated solvable groups from a combinatorial group theory perspective.​

Reviews

From the reviews:

“This work by Bencsáth (Manhattan College) and CUNY colleagues begins with 25 pages of combinatorial group theory preliminaries … . Recommended. Upper-division undergraduates and above.” (D. V. Feldman, Choice, Vol. 50 (8), April, 2013)

Table of contents (7 chapters)

  • Preliminaries

    Bencsáth, Katalin A. (et al.)

    Pages 1-4

  • Tools: Presentations and Their Calculus

    Bencsáth, Katalin A. (et al.)

    Pages 5-7

  • Constructions

    Bencsáth, Katalin A. (et al.)

    Pages 9-18

  • Representations and a Theorem of Krasner and Kaloujnine

    Bencsáth, Katalin A. (et al.)

    Pages 19-24

  • The Bieri–Strebel Theorems

    Bencsáth, Katalin A. (et al.)

    Pages 25-30

Buy this book

eBook $34.99
price for USA (gross)
  • ISBN 978-1-4614-5450-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.95
price for USA
  • ISBN 978-1-4614-5449-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Lectures on Finitely Generated Solvable Groups
Authors
Series Title
SpringerBriefs in Mathematics
Copyright
2013
Publisher
Springer-Verlag New York
Copyright Holder
Katalin A. Bencsath, Marianna C. Bonanome, Margaret H. Dean, Marcos Zyman
eBook ISBN
978-1-4614-5450-2
DOI
10.1007/978-1-4614-5450-2
Softcover ISBN
978-1-4614-5449-6
Series ISSN
2191-8198
Edition Number
1
Number of Pages
XIV, 52
Topics