Titlebook: Generators and Relations for Discrete Groups; H. S. M. Coxeter,W. O. J. Moser Book 1980Latest edition Springer-Verlag GmbH Germany 1980 Di

迅速成长

The Symmetric, Alternating, and other Special Groups,g generators and relations for S. can be carried over almost unchanged for a certain infinite group, first studied by . (1926); accordingly, we begin by describing this so-called braid group. The symmetric group (§ 6.2) has a subgroup A., of index 2 (§ 6.3), which is particularly interesting because, when . > 4, it is simple.

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思考

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Hyperbolic Tessellations and Fundamental Groups,After describing the regular tessellations {.} (which are simply-connected topological polyhedra), we shall derive the fundamental groups (§ 3.5, p. 24) for closed surfaces of arbitrary characteristic. From the present standpoint, non-orientable surfaces are easier than orientable surfaces; accordingly, we consider them in this unusual order.

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轻浮思想

Critical Analysis of Science Textbooksverted this into a mechanical technique, a useful tool with a wide range of applications. In § 2.1 we describe this algorithm, in § 2.2 we use it to determine an abstract definition for a given finite group, and in § 2.3 we describe some additional computation, performed alongside the enumeration, w

围裙

Binomial and Normal Distributions 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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