群与对称

出版时间：2011-4  出版社：世界图书出版公司  作者：阿姆斯壮  页数：186  
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内容概要

　　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.

作者简介

作者：（英国）阿姆斯壮（M.A.Armstrong）

书籍目录

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

章节摘录

版权页：插图：

编辑推荐

《群与对称(英文版)》是由世界图书出版公司出版的。

用户评论 (总计3条)

•   很基础的书，适合大学新生学代数时读一读
•   老师推荐的好书，印刷。。。。。我都没力气说它了
•   通俗易懂 更好的群的几何看法