Generators and relations for discrete groups
Author(s)
Bibliographic Information
Generators and relations for discrete groups
（Ergebnisse der Mathematik und ihrer Grenzgebiete, Bd. 14）
Springer-Verlag, 1972
3rd ed
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Note
Bibliography: p. 143-156
Includes index
Description and Table of Contents
Description
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.
Table of Contents
1. Cyclic, Dicyclic and Metacyclic Groups.- 2. Systematic Enumeration of Cosets.- 3. Graphs, Maps and Cayley Diagrams.- 4. Abstract Crystallography.- 5. Hyperbolic Tessellations and Fundamental Groups.- 6. The Symmetric, Alternating, and other Special Groups.- 7. Modular and Linear Fractional Groups.- 8. Regular Maps.- 9. Groups Generated by Reflections.- Tables 1-12.
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