Skip to main content
SpringerLink
Log in
Book cover

Groups and Symmetry

  • Textbook
  • © 1988

Overview

Authors:
  1. M. A. Armstrong

    1. Department of Mathematical Sciences, University of Durham, Durham, England

    View author publications

    You can also search for this author in PubMed   Google Scholar

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

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 49.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 64.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 64.95
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (28 chapters)

  1. Front Matter

    Pages i-xi
    Download chapter PDF

  2. Symmetries of the Tetrahedron

    • M. A. Armstrong
    Pages 1-5

  3. Axioms

    • M. A. Armstrong
    Pages 6-10

  4. Numbers

    • M. A. Armstrong
    Pages 11-14

  5. Dihedral Groups

    • M. A. Armstrong
    Pages 15-19

  6. Subgroups and Generators

    • M. A. Armstrong
    Pages 20-25

  7. Permutations

    • M. A. Armstrong
    Pages 26-31

  8. Isomorphisms

    • M. A. Armstrong
    Pages 32-36

  9. Plato’s Solids and Cayley’s Theorem

    • M. A. Armstrong
    Pages 37-43

  10. Matrix Groups

    • M. A. Armstrong
    Pages 44-51

  11. Products

    • M. A. Armstrong
    Pages 52-56

  12. Lagrange’s Theorem

    • M. A. Armstrong
    Pages 57-60

  13. Partitions

    • M. A. Armstrong
    Pages 61-67

  14. Cauchy’s Theorem

    • M. A. Armstrong
    Pages 68-72

  15. Conjugacy

    • M. A. Armstrong
    Pages 73-78

  16. Quotient Groups

    • M. A. Armstrong
    Pages 79-85

  17. Homomorphisms

    • M. A. Armstrong
    Pages 86-90

  18. Actions, Orbits, and Stabilizers

    • M. A. Armstrong
    Pages 91-97

  19. Counting Orbits

    • M. A. Armstrong
    Pages 98-103

  20. Finite Rotation Groups

    • M. A. Armstrong
    Pages 104-112
Back to top

Keywords

About this book

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.

Reviews

M.A. Armstrong

Groups and Symmetry

"This book is a gentle introductory text on group theory and its application to the measurement of symmetry. It covers most of the material that one might expect to see in an undergraduate course . . . The theory is amplified, exemplified and properly related to what this part of algebra is really for by discussion of a wide variety of geometrical phenomena in which groups measure symmetry. Overall, the author’s plan, to base his treatment on the premise that groups and symmetry go together, is a very good one, and the book deserves to succeed."—MATHEMATICAL REVIEWS

Authors and Affiliations

  • Department of Mathematical Sciences, University of Durham, Durham, England

    M. A. Armstrong

Bibliographic Information

  • Book Title: Groups and Symmetry

  • Authors: M. A. Armstrong

  • Series Title: Undergraduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4757-4034-9

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York 1988

  • Hardcover ISBN: 978-0-387-96675-5Published: 25 October 1988

  • Softcover ISBN: 978-1-4419-3085-9Published: 01 December 2010

  • eBook ISBN: 978-1-4757-4034-9Published: 14 March 2013

  • Series ISSN: 0172-6056

  • Series E-ISSN: 2197-5604

  • Edition Number: 1

  • Number of Pages: XI, 187

  • Topics: Group Theory and Generalizations

Publish with us

Policies and ethics

Back to top

Search

Navigation