| 书目名称 | Generators and Relations for Discrete Groups | | 编辑 | H. S. M. Coxeter,W. O. J. Moser | | 视频video | | | 丛书名称 | Ergebnisse der Mathematik und Ihrer Grenzgebiete. 1. Folge | | 图书封面 |  | | 描述 | 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 gener | | 出版日期 | Book 1957 | | 关键词 | Permutation; algebra; finite group; transformation | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-662-25739-5 | | isbn_softcover | 978-3-662-23654-3 | | isbn_ebook | 978-3-662-25739-5 | | copyright | Springer-Verlag Berlin Heidelberg 1957 |
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发表于 2025-3-21 19:56:15
