A Course in the Theory of Groups

  • Derek J. S. Robinson

Part of the Graduate Texts in Mathematics book series (GTM, volume 80)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Derek J. S. Robinson
    Pages 1-43
  3. Derek J. S. Robinson
    Pages 44-60
  4. Derek J. S. Robinson
    Pages 61-89
  5. Derek J. S. Robinson
    Pages 90-116
  6. Derek J. S. Robinson
    Pages 117-152
  7. Derek J. S. Robinson
    Pages 153-184
  8. Derek J. S. Robinson
    Pages 185-205
  9. Derek J. S. Robinson
    Pages 206-244
  10. Derek J. S. Robinson
    Pages 245-275
  11. Derek J. S. Robinson
    Pages 276-300
  12. Derek J. S. Robinson
    Pages 301-341
  13. Derek J. S. Robinson
    Pages 342-370
  14. Derek J. S. Robinson
    Pages 371-400
  15. Derek J. S. Robinson
    Pages 401-432
  16. Derek J. S. Robinson
    Pages 433-460
  17. Back Matter
    Pages 461-484

About this book

Introduction

" A group is defined by means of the laws of combinations of its symbols," according to a celebrated dictum of Cayley. And this is probably still as good a one-line explanation as any. The concept of a group is surely one of the central ideas of mathematics. Certainly there are a few branches of that science in which groups are not employed implicitly or explicitly. Nor is the use of groups confined to pure mathematics. Quantum theory, molecular and atomic structure, and crystallography are just a few of the areas of science in which the idea of a group as a measure of symmetry has played an important part. The theory of groups is the oldest branch of modern algebra. Its origins are to be found in the work of Joseph Louis Lagrange (1736-1813), Paulo Ruffini (1765-1822), and Evariste Galois (1811-1832) on the theory of algebraic equations. Their groups consisted of permutations of the variables or of the roots of polynomials, and indeed for much of the nineteenth century all groups were finite permutation groups. Nevertheless many of the fundamental ideas of group theory were introduced by these early workers and their successors, Augustin Louis Cauchy (1789-1857), Ludwig Sylow (1832-1918), Camille Jordan (1838-1922) among others. The concept of an abstract group is clearly recognizable in the work of Arthur Cayley (1821-1895) but it did not really win widespread acceptance until Walther von Dyck (1856-1934) introduced presentations of groups.

Keywords

Abelian group Finite Group theory Permutation algebra automorphism cohomology finite group group group action mathematics mutation presentation semigroup symmetry

Authors and affiliations

  • Derek J. S. Robinson
    • 1
  1. 1.Department of MathematicsUniversity of Illinois at Urbana-ChampaignUrbanaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4684-0128-8
  • Copyright Information Springer-Verlag New York 1993
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-94092-2
  • Online ISBN 978-1-4684-0128-8
  • Series Print ISSN 0072-5285
  • About this book