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  • Textbook
  • © 1985

Finite Reflection Groups

Part of the book series: Graduate Texts in Mathematics (GTM, volume 99)

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  • ISBN: 978-1-4757-1869-0
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Table of contents (8 chapters)

  1. Front Matter

    Pages i-x
  2. Preliminaries

    • L. C. Grove, C. T. Benson
    Pages 1-4
  3. Finite Groups in Two and Three Dimensions

    • L. C. Grove, C. T. Benson
    Pages 5-26
  4. Fundamental Regions

    • L. C. Grove, C. T. Benson
    Pages 27-33
  5. Coxeter Groups

    • L. C. Grove, C. T. Benson
    Pages 34-52
  6. Classification of Coxeter Groups

    • L. C. Grove, C. T. Benson
    Pages 53-82
  7. Generators and Relations for Coxeter Groups

    • L. C. Grove, C. T. Benson
    Pages 83-103
  8. Invariants

    • L. C. Grove, C. T. Benson
    Pages 104-123
  9. Postlude

    • L. C. Grove, C. T. Benson
    Pages 124-126
  10. Back Matter

    Pages 127-133

About this book

Chapter 1 introduces some of the terminology and notation used later and indicates prerequisites. Chapter 2 gives a reasonably thorough account of all finite subgroups of the orthogonal groups in two and three dimensions. The presentation is somewhat less formal than in succeeding chapters. For instance, the existence of the icosahedron is accepted as an empirical fact, and no formal proof of existence is included. Throughout most of Chapter 2 we do not distinguish between groups that are "geo­ metrically indistinguishable," that is, conjugate in the orthogonal group. Very little of the material in Chapter 2 is actually required for the sub­ sequent chapters, but it serves two important purposes: It aids in the development of geometrical insight, and it serves as a source of illustrative examples. There is a discussion offundamental regions in Chapter 3. Chapter 4 provides a correspondence between fundamental reflections and funda­ mental regions via a discussion of root systems. The actual classification and construction of finite reflection groups takes place in Chapter 5. where we have in part followed the methods of E. Witt and B. L. van der Waerden. Generators and relations for finite reflection groups are discussed in Chapter 6. There are historical remarks and suggestions for further reading in a Post lude.

Keywords

  • Finite
  • Groups
  • Invariant
  • Point group
  • boundary element method
  • classification
  • construction
  • development
  • eXist
  • finite group
  • form
  • formal proof
  • group
  • presentation
  • proof

Authors and Affiliations

  • Department of Mathematics, University of Arizona, Tucson, USA

    L. C. Grove, C. T. Benson

Bibliographic Information

  • Book Title: Finite Reflection Groups

  • Authors: L. C. Grove, C. T. Benson

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4757-1869-0

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York 1985

  • Hardcover ISBN: 978-0-387-96082-1

  • Softcover ISBN: 978-1-4419-3072-9

  • eBook ISBN: 978-1-4757-1869-0

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 2

  • Number of Pages: X, 136

  • Additional Information: Originally published by Bogden & Quigley, 1971

  • Topics: Group Theory and Generalizations

Buying options

eBook USD 44.99
Price excludes VAT (USA)
  • ISBN: 978-1-4757-1869-0
  • 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 59.99
Price excludes VAT (USA)
Hardcover Book USD 84.99
Price excludes VAT (USA)