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Groups and Symmetry

  • M. A. Armstrong

Part of the Undergraduate Texts in Mathematics book series (UTM)

Table of contents

  1. Front Matter
    Pages i-xi
  2. M. A. Armstrong
    Pages 1-5
  3. M. A. Armstrong
    Pages 6-10
  4. M. A. Armstrong
    Pages 11-14
  5. M. A. Armstrong
    Pages 15-19
  6. M. A. Armstrong
    Pages 20-25
  7. M. A. Armstrong
    Pages 26-31
  8. M. A. Armstrong
    Pages 32-36
  9. M. A. Armstrong
    Pages 37-43
  10. M. A. Armstrong
    Pages 44-51
  11. M. A. Armstrong
    Pages 52-56
  12. M. A. Armstrong
    Pages 57-60
  13. M. A. Armstrong
    Pages 61-67
  14. M. A. Armstrong
    Pages 68-72
  15. M. A. Armstrong
    Pages 73-78
  16. M. A. Armstrong
    Pages 79-85
  17. M. A. Armstrong
    Pages 86-90
  18. M. A. Armstrong
    Pages 91-97
  19. M. A. Armstrong
    Pages 98-103
  20. M. A. Armstrong
    Pages 104-112
  21. M. A. Armstrong
    Pages 113-118
  22. M. A. Armstrong
    Pages 119-124
  23. M. A. Armstrong
    Pages 125-130
  24. M. A. Armstrong
    Pages 131-135
  25. M. A. Armstrong
    Pages 136-144
  26. M. A. Armstrong
    Pages 145-154
  27. M. A. Armstrong
    Pages 155-165
  28. M. A. Armstrong
    Pages 166-172
  29. M. A. Armstrong
    Pages 173-180
  30. Back Matter
    Pages 181-187

About this book

Introduction

Groups are important because they measure symmetry. This text, designed for undergraduate mathematics students, provides a gentle introduction to the highlights of elementary group theory. Written in an informal style, the material is divided into short sections each of which deals with an important result or a new idea. Throughout the book, the emphasis is placed on concrete examples, many of them geometrical in nature, so that finite rotation groups and the seventeen wallpaper groups are treated in detail alongside theoretical results such as Lagrange's theorem, the Sylow theorems, and the classification theorem for finitely generated abelian groups. A novel feature at this level is a proof of the Nielsen-Schreier theorem, using group actions on trees. There are more than three hundred exercises and approximately sixty illustrations to help develop the student's intuition.

Keywords

Abelian group Group theory Lattice Point group automorphism group action

Authors and affiliations

  • M. A. Armstrong
    • 1
  1. 1.Department of Mathematical SciencesUniversity of DurhamDurhamEngland

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-4034-9
  • Copyright Information Springer-Verlag New York 1988
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-3085-9
  • Online ISBN 978-1-4757-4034-9
  • Series Print ISSN 0172-6056
  • Buy this book on publisher's site