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  • Textbook
  • © 1988

Groups and Symmetry

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

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  • ISBN: 978-1-4757-4034-9
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Softcover Book USD 64.95
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Table of contents (28 chapters)

  1. Front Matter

    Pages i-xi
  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

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.

Keywords

  • Abelian group
  • Group theory
  • Lattice
  • Point group
  • automorphism
  • group action

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: 978-0-387-96675-5

  • Softcover ISBN: 978-1-4419-3085-9

  • eBook ISBN: 978-1-4757-4034-9

  • Series ISSN: 0172-6056

  • Series E-ISSN: 2197-5604

  • Edition Number: 1

  • Number of Pages: XI, 187

  • Topics: Group Theory and Generalizations

Buying options

eBook USD 49.99
Price excludes VAT (USA)
  • ISBN: 978-1-4757-4034-9
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 64.95
Price excludes VAT (USA)
Hardcover Book USD 64.95
Price excludes VAT (USA)