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  • Book
  • © 1972

Generators and Relations for Discrete Groups

Authors:

  1. H. S. M. Coxeter
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    You can also search for this author in PubMed   Google Scholar

  2. W. O. J. Moser
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Part of the book series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge (MATHE2, volume 14)

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Table of contents (9 chapters)

  1. Front Matter

    Pages N1-IX
    PDF

  2. Cyclic, Dicyclic and Metacyclic Groups

    • H. S. M. Coxeter, W. O. J. Moser
    Pages 1-12

  3. Systematic Enumeration of Cosets

    • H. S. M. Coxeter, W. O. J. Moser
    Pages 12-18

  4. Graphs, Maps and Cayley Diagrams

    • H. S. M. Coxeter, W. O. J. Moser
    Pages 18-32

  5. Abstract Crystallography

    • H. S. M. Coxeter, W. O. J. Moser
    Pages 32-52

  6. Hyperbolic Tessellations and Fundamental Groups

    • H. S. M. Coxeter, W. O. J. Moser
    Pages 52-61

  7. The Symmetric, Alternating, and other Special Groups

    • H. S. M. Coxeter, W. O. J. Moser
    Pages 61-82

  8. Modular and Linear Fractional Groups

    • H. S. M. Coxeter, W. O. J. Moser
    Pages 83-101

  9. Regular Maps

    • H. S. M. Coxeter, W. O. J. Moser
    Pages 101-117

  10. Groups Generated by Reflections

    • H. S. M. Coxeter, W. O. J. Moser
    Pages 117-133

  11. Back Matter

    Pages 134-164
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About this book

When we began to consider the scope of this book, we envisaged a catalogue supplying at least one abstract definition for any finitely­ generated group that the reader might propose. But we soon realized that more or less arbitrary restrietions are necessary, because interesting groups are so numerous. For permutation groups of degree 8 or less (i.e., .subgroups of 2: ), the reader cannot do better than consult the 8 tables of ]OSEPHINE BURNS (1915), while keeping an eye open for misprints. Our own tables (on pages 134-142) deal with groups of low order, finite and infinite groups ()f congruent transformations, symmetrie and alternating groups, linear fractional groups, and groups generated by reflections in real Euclidean space of any number of dimensions. The best substitute for a more extensive catalogue is the description (in Chapter 2) of a method whereby the reader can easily work out his own abstract definition for almost any given finite group. This method is sufficiently mechanical for the use of an electronic computer.
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Keywords

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Bibliographic Information

  • Book Title: Generators and Relations for Discrete Groups

  • Authors: H. S. M. Coxeter, W. O. J. Moser

  • Series Title: Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge

  • DOI: https://doi.org/10.1007/978-3-662-21946-1

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1972

  • eBook ISBN: 978-3-662-21946-1Published: 11 November 2013

  • Edition Number: 3

  • Number of Pages: IX, 164

  • Number of Illustrations: 74 b/w illustrations

  • Topics: Algebra

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eBook USD 14.99
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  • Available as PDF
  • Read on any device
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  • Own it forever

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