Description: Generators and Relations for Discrete Groups, Paperback by Coxeter, Harold Scott Macdonald; Moser, William O. J., ISBN 3662236540, ISBN-13 9783662236543, Brand New, Free shipping in the US 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 e ), the reader cannot do better than consult the 8 tables of JosEPHINE BuRNS (1915), while keeping an eye open for misprints. Our own tables (on pages 134-143) deal with groups of low order, finiteandinfinite 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 foramoreextensive 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. There is also a topological method (Chapter 3), suitable not only for groups of low order but also for some infinite groups. This involves choosing a set of generators, constructing a certain graph (the Cayley diagram or DEHNsehe Gruppenbild), and embedding the graph into a surface. Cases in which the surface is a sphere or a plane are described in Chapter 4, where we obtain algebraically, and verify topologically, an abstract definition for each of the 17 space groups of two-dimensional crystallography.
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Book Title: Generators and Relations for Discrete Groups
Number of Pages: VIII, 155 Pages
Publication Name: Generators and Relations for Discrete Groups
Language: English
Publisher: Springer Berlin / Heidelberg
Publication Year: 1957
Subject: Algebra / General
Type: Textbook
Item Weight: 9.2 Oz
Author: H. S. M. Coxeter, William O. J. Moser
Item Length: 9.3 in
Subject Area: Mathematics
Item Width: 6.1 in
Series: Ergebnisse Der Mathematik Und Ihrer Grenzgebiete. 1. Folge Ser.
Format: Trade Paperback
