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

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書目名稱Generators and Relations for Discrete Groups
編輯H. S. M. Coxeter,W. O. J. Moser
視頻videohttp://file.papertrans.cn/383/382373/382373.mp4
叢書名稱Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge
圖書封面Titlebook: Generators and Relations for Discrete Groups;  H. S. M. Coxeter,W. O. J. Moser Book 1980Latest edition Springer-Verlag GmbH Germany 1980 Di
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 es), the reader cannot do better than consult the tables of JosEPHINE BuRNS (1915), while keeping an eye open for misprints. Our own tables (on pages 134-142) deal with groups of low order, finite and infinite 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 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.
出版日期Book 1980Latest edition
關(guān)鍵詞Diskrete Gruppe; Finite; Permutation; Scope; Visage; computer; finite group; form; group; mutation; reflection
版次4
doihttps://doi.org/10.1007/978-3-662-21943-0
isbn_softcover978-3-662-21945-4
isbn_ebook978-3-662-21943-0
copyrightSpringer-Verlag GmbH Germany 1980
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rated 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 es), the reader cannot do better than consult the tables of JosEPHINE Bu
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Critical Analysis of Science Textbooksetermine an abstract definition for a given finite group, and in § 2.3 we describe some additional computation, performed alongside the enumeration, which determines an abstract definition for the subgroup.
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Elizabeth Mackinlay,Renée Mickelburghrove 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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Book 1980Latest editionp 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 es), the reader cannot do better than consult the tables of JosEPHINE BuRNS (1915)
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