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The History of Combinatorial Group Theory

A Case Study in the History of Ideas

  • Book
  • © 1982

Overview

Authors:
  1. Bruce Chandler

    1. The College of Staten Island of The City University of New York, Staten Island, USA

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  2. Wilhelm Magnus

    1. New Rochelle, USA

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    You can also search for this author in PubMed   Google Scholar

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

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Table of contents (25 chapters)

  1. Front Matter

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

    1. Front Matter

      Pages 1-1
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    2. Introduction to Part I

      • Bruce Chandler, Wilhelm Magnus
      Pages 3-4

    3. The Foundation: Dyck’s Group-Theoretical Studies

      • Bruce Chandler, Wilhelm Magnus
      Pages 5-10

    4. The Origin: The Theory of Discontinuous Groups

      • Bruce Chandler, Wilhelm Magnus
      Pages 11-13

    5. Motivation: The Fundamental Groups of Topological Spaces

      • Bruce Chandler, Wilhelm Magnus
      Pages 14-21

    6. The Graphical Representation of Groups

      • Bruce Chandler, Wilhelm Magnus
      Pages 22-28

    7. Precursors of Later Developments

      • Bruce Chandler, Wilhelm Magnus
      Pages 29-50

    8. Summary

      • Bruce Chandler, Wilhelm Magnus
      Pages 51-57

    9. Modes of Communication. Growth and Distribution of Research in Group Theory

      • Bruce Chandler, Wilhelm Magnus
      Pages 58-67

    10. Biographical Notes

      • Bruce Chandler, Wilhelm Magnus
      Pages 68-70

    11. Notes on Terminology and Definitions

      • Bruce Chandler, Wilhelm Magnus
      Pages 71-74

    12. Sources

      • Bruce Chandler, Wilhelm Magnus
      Pages 75-76

  3. The Emergence of Combinatorial Group Theory as an Independent Field

    1. Front Matter

      Pages 77-77
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    2. Introduction to Part II

      • Bruce Chandler, Wilhelm Magnus
      Pages 79-80

    3. Free Groups and Their Automorphisms

      • Bruce Chandler, Wilhelm Magnus
      Pages 81-90

    4. The Reidemeister—Schreier Method

      • Bruce Chandler, Wilhelm Magnus
      Pages 91-101

    5. Free Products and Free Products with Amalgamations

      • Bruce Chandler, Wilhelm Magnus
      Pages 102-112

    6. One-Relator Groups

      • Bruce Chandler, Wilhelm Magnus
      Pages 113-121

    7. Metabelian Groups and Related Topics

      • Bruce Chandler, Wilhelm Magnus
      Pages 122-140
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Keywords

About this book

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.

Authors and Affiliations

  • The College of Staten Island of The City University of New York, Staten Island, USA

    Bruce Chandler

  • New Rochelle, USA

    Wilhelm Magnus

Bibliographic Information

  • Book Title: The History of Combinatorial Group Theory

  • Book Subtitle: A Case Study in the History of Ideas

  • Authors: Bruce Chandler, Wilhelm Magnus

  • Series Title: Studies in the History of Mathematics and Physical Sciences

  • DOI: https://doi.org/10.1007/978-1-4613-9487-7

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York Inc. 1982

  • Softcover ISBN: 978-1-4613-9489-1Published: 14 December 2011

  • eBook ISBN: 978-1-4613-9487-7Published: 06 December 2012

  • Series ISSN: 0172-570X

  • Edition Number: 1

  • Number of Pages: VIII, 234

  • Topics: Group Theory and Generalizations

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