Generators and Relations for Discrete Groups

Harold S.M. Coxeter, William O. J. Moser (Autoren)

Buch | Softcover

IX, 172 Seiten

2017 | 4. Fourth Edition 1980
Springer Berlin (Verlag)
978-3-662-21945-4 (ISBN)

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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 restrictions are necessary, because interesting groups are so numerous. For permutation groups of degree 8 or less (i.e.' .subgroups of es), the reader cannot do better than consult the tables of JosEPHINE 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 of congruent transformations, symmetric 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.

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.- Appendix for Chapter 2.

Erscheinungsdatum	01.09.2016
Reihe/Serie	Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge
Zusatzinfo	IX, 172 p. 2 illus.
Verlagsort	Berlin
Sprache	englisch
Maße	170 x 244 mm
Themenwelt	Mathematik / Informatik ► Mathematik
Schlagworte	Computer • Diskrete Gruppe • Finite • finite group • Form • Group • Groups and group theory • Group Theory and Generalizations • mathematics and statistics • Mutation • Permutation • reflection • Scope • Transformation • visage
ISBN-10	3-662-21945-X / 366221945X
ISBN-13	978-3-662-21945-4 / 9783662219454
Zustand	Neuware