Titlebook: Generators and Relations for Discrete Groups; H. S. M. Coxeter,W. O. J. Moser Book 1957 Springer-Verlag Berlin Heidelberg 1957 Permutation

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Book 1957 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 gener

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shrill

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Cyclic, Dicyclic and Metacyclic Groups,ahedral group, respectively. Observing that the standard treatises use the term . group in two distinct senses, we exhibit both kinds among the groups of order less than 32, whose simplest known abstract definitions are collected in Table 1.

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The Symmetric, Alternating, and other Special Groups,by describing this so-called braid group. The symmetric group (§ 6.2, p. 64) has a subgroup A., of index 2 (§ 6.3, p. 66), which is particularly interesting because, when . > 4, it is simple. In § 6.4, p. 67, we exhibit the groups S., A., S. and A. as members of the family of polyhedral groups (.),defined by ..