Titlebook: Generators and Relations for Discrete Groups; H. S. M. Coxeter,W. O. J. Moser Book 19723rd edition Springer-Verlag Berlin Heidelberg 1972

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Systematic Enumeration of Cosets, definition for a given finite group. In § 2.4 we use it to find whether a given subgroup of an abstract group is normal. Finally, in § 2.5 we see how it helps in determining properties of new abstract groups.

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Graphs, Maps and Cayley Diagrams,nguish the edges associated with different generators (see . 1911, pp. 423–427 and the frontispiece). Instead, for the sake of easier printing, we use lines drawn in various styles: ordinary, broken, dotted, etc. After suitably embedding the graph into a surface, we obtain a map from which a set of defining relations for the group may be read off.

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Groups Generated by Reflections,prove that the generators may always be represented by real affine reflections, thus preparing the ground for a complete enumeration of the finite groups. Then we shall describe some of their remarkable properties.

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Springer-Verlag Berlin Heidelberg 1972

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