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The History of Combinatorial Group Theory

A Case Study in the History of Ideas

  • Bruce Chandler
  • Wilhelm Magnus

Part of the Studies in the History of Mathematics and Physical Sciences book series (HISTORY, volume 9)

Table of contents

  1. Front Matter
    Pages i-viii
  2. The Beginning of Combinatorial Group Theory

    1. Front Matter
      Pages 1-1
    2. Bruce Chandler, Wilhelm Magnus
      Pages 3-4
    3. Bruce Chandler, Wilhelm Magnus
      Pages 5-10
    4. Bruce Chandler, Wilhelm Magnus
      Pages 11-13
    5. Bruce Chandler, Wilhelm Magnus
      Pages 14-21
    6. Bruce Chandler, Wilhelm Magnus
      Pages 22-28
    7. Bruce Chandler, Wilhelm Magnus
      Pages 29-50
    8. Bruce Chandler, Wilhelm Magnus
      Pages 51-57
    9. Bruce Chandler, Wilhelm Magnus
      Pages 68-70
    10. Bruce Chandler, Wilhelm Magnus
      Pages 71-74
    11. Bruce Chandler, Wilhelm Magnus
      Pages 75-76
  3. The Emergence of Combinatorial Group Theory as an Independent Field

    1. Front Matter
      Pages 77-77
    2. Bruce Chandler, Wilhelm Magnus
      Pages 79-80
    3. Bruce Chandler, Wilhelm Magnus
      Pages 81-90
    4. Bruce Chandler, Wilhelm Magnus
      Pages 91-101
    5. Bruce Chandler, Wilhelm Magnus
      Pages 102-112
    6. Bruce Chandler, Wilhelm Magnus
      Pages 113-121
    7. Bruce Chandler, Wilhelm Magnus
      Pages 122-140
    8. Bruce Chandler, Wilhelm Magnus
      Pages 141-156
    9. Bruce Chandler, Wilhelm Magnus
      Pages 157-161
    10. Bruce Chandler, Wilhelm Magnus
      Pages 162-174
    11. Bruce Chandler, Wilhelm Magnus
      Pages 175-180
    12. Bruce Chandler, Wilhelm Magnus
      Pages 181-186
    13. Bruce Chandler, Wilhelm Magnus
      Pages 187-192
    14. Bruce Chandler, Wilhelm Magnus
      Pages 193-199
    15. Bruce Chandler, Wilhelm Magnus
      Pages 200-206
  4. Back Matter
    Pages 207-234

About this book

Introduction

One of the pervasive phenomena in the history of science is the development of independent disciplines from the solution or attempted solutions of problems in other areas of science. In the Twentieth Century, the creation of specialties witqin the sciences has accelerated to the point where a large number of scientists in any major branch of science cannot understand the work of a colleague in another subdiscipline of his own science. Despite this fragmentation, the development of techniques or solutions of problems in one area very often contribute fundamentally to solutions of problems in a seemingly unrelated field. Therefore, an examination of this phenomenon of the formation of independent disciplines within the sciences would contrib­ ute to the understanding of their evolution in modern times. We believe that in this context the history of combinatorial group theory in the late Nineteenth Century and the Twentieth Century can be used effectively as a case study. It is a reasonably well-defined independent specialty, and yet it is closely related to other mathematical disciplines. The fact that combinatorial group theory has, so far, not been influenced by the practical needs of science and technology makes it possible for us to use combinatorial group theory to exhibit the role of the intellectual aspects of the development of mathematics in a clearcut manner. There are other features of combinatorial group theory which appear to make it a reasona­ ble choice as the object of a historical study.

Keywords

Abelian group Definierende Relation Erzeugendensystem Group theory Gruppe (Math.) History Präsentation (Math.)

Authors and affiliations

  • Bruce Chandler
    • 1
  • Wilhelm Magnus
    • 2
  1. 1.The College of Staten Island of The City University of New YorkStaten IslandUSA
  2. 2.New RochelleUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4613-9487-7
  • Copyright Information Springer-Verlag New York 1982
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4613-9489-1
  • Online ISBN 978-1-4613-9487-7
  • Series Print ISSN 0172-570X
  • Buy this book on publisher's site