Lectures on Finitely Generated Solvable Groups

  • Katalin A. Bencsath
  • Marianna C. Bonanome
  • Margaret H. Dean
  • Marcos Zyman
Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Katalin A. Bencsáth, Marianna C. Bonanome, Margaret H. Dean, Marcos Zyman
    Pages 1-4
  3. Katalin A. Bencsáth, Marianna C. Bonanome, Margaret H. Dean, Marcos Zyman
    Pages 5-7
  4. Katalin A. Bencsáth, Marianna C. Bonanome, Margaret H. Dean, Marcos Zyman
    Pages 9-18
  5. Katalin A. Bencsáth, Marianna C. Bonanome, Margaret H. Dean, Marcos Zyman
    Pages 19-24
  6. Katalin A. Bencsáth, Marianna C. Bonanome, Margaret H. Dean, Marcos Zyman
    Pages 25-30
  7. Katalin A. Bencsáth, Marianna C. Bonanome, Margaret H. Dean, Marcos Zyman
    Pages 31-34
  8. Katalin A. Bencsáth, Marianna C. Bonanome, Margaret H. Dean, Marcos Zyman
    Pages 35-43
  9. Back Matter
    Pages 45-52

About this book

Introduction

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.​

Keywords

Baumslag embedding theorem Bieri-Strebel theorems amalgamated and wreath products combinatorial group theory finitely generated solvable groups nilpotent, polycyclic, and metabelian groups

Authors and affiliations

  • Katalin A. Bencsath
    • 1
  • Marianna C. Bonanome
    • 2
  • Margaret H. Dean
    • 3
  • Marcos Zyman
    • 4
  1. 1., Mathematics and Computer ScienceManhattan CollegeRiverdaleUSA
  2. 2., Applied Math and Computer ScienceNew York City College of TechnologyBrooklynUSA
  3. 3.The City University of New York, Department of MathematicsBorough of Manhattan Community CollegeNew YorkUSA
  4. 4.The City University of New York, Department of MathematicsBorough of Manhattan Community CollegeNew YorkUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-5450-2
  • Copyright Information Katalin A. Bencsath, Marianna C. Bonanome, Margaret H. Dean, Marcos Zyman 2013
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-5449-6
  • Online ISBN 978-1-4614-5450-2
  • Series Print ISSN 2191-8198
  • Series Online ISSN 2191-8201
  • About this book