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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范围广

Regular Maps,it was remarked by . (1926, p. 238) that “There is no regular map of 8, 10 or 11 hexagons, no map of 14 hexagons although there are maps of 7, 21 and 28 hexagons”. The expression that he sought is our 8.42 (. 1911, p. 418). The first mention of maps on non-orientable surfaces seems to have been by .

水土

Book 19723rd editioner 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.

tenosynovitis

f 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.978-3-662-21946-1

ADJ

https://doi.org/10.1007/978-3-031-39151-4it was remarked by . (1926, p. 238) that “There is no regular map of 8, 10 or 11 hexagons, no map of 14 hexagons although there are maps of 7, 21 and 28 hexagons”. The expression that he sought is our 8.42 (. 1911, p. 418). The first mention of maps on non-orientable surfaces seems to have been by .

Factorable

Cyclic, Dicyclic and Metacyclic Groups,s us to adjoin a new element so as to obtain a larger group; ., the cyclic and non-cyclic groups of order 4 yield the quaternion group and the tetrahedral group, respectively. Observing that the standard treatises use the term . group in two distinct senses, we exhibit both kinds among the groups of

Factorable

Systematic Enumeration of Cosets,verted this method into an almost mechanical technique, a useful tool with a wide range of applications. In § 2.1 we apply it to determine an abstract 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

Obedient

Graphs, Maps and Cayley Diagrams, represent the elements of the group while certain sets of edges are associated with the generators. . (1878a, b) proposed the use of colours to distinguish the edges associated with different generators (see . 1911, pp. 423–427 and the frontispiece). Instead, for the sake of easier printing, we use

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