文件名称:群与对称(英文版)[(英)阿姆斯壮 著] 2011年版

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群与对称(英文版) 出版时间:2011年版 内容简介   《群与对称》讲述了 numbers measure size, groups measure symmetry. the first statement comes as no surprise; after all, that is what numbers are for. the second will be exploited here in an attempt to introduce the vocabulary and some of the highlights of elementary group theory. a word about content and style seems appropriate. in this volume, the emphasis is on examples throughout, with a weighting towards the symmetry groups of solids and patterns. almost all the topics have been chosen so as to show groups in their most natural role, acting on (or permuting) the members ora set, whether it be the diagonals of a cube, the edges of a tree, or even some collection of subgroups of the given group. the material is divided into twenty-eight short chapters, each of which introduces a new result or idea.a glance at the contents will show that most of the mainstays of a first course arc here. the theorems of lagrange, cauchy, and sylow all have a chapter to themselves, as do the classifcation of finitely generated abelian groups, the enumeration of the finite rotation groups and the plane crystallographic groups, and the nielsen-schreier theorem. 目录 preface chapter 1 symmetries of the tetrahedron chapter 2 axioms chapter 3 numbers chapter 4 dihedral groups chapter 5 subgroups and generators chapter 6 permutations chapter 7 isomorphisms chapter 8 plato‘s solids and cayley’s theorem chapter 9 matrix groups chapter 10 products chapter 11 lagrange‘s theorem chapter 12 partitions chapter 13 cauehy’s theorem chapter 14 coujugacy chapter 15 quotient groups chapter 16 homomorphisms chapter 17 actions, orbits, and stabilizers chapter 18 counting orbits chapter 19 finite rotation groups chapter 20 the sylow theorems chapter 21 finitely generated abelian groups chapter 22 row and column operations chapter 23 automorphisms chapter 24 the euclidean group chapter 25 lattices and point groups chapter 26 wallpaper patterns chapter 27 free groups and presentations chapter 28 trees and the nielsen-schreier theorem bibliography index
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