群與對稱

內(nèi)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.

作者簡介

作者：（英國）阿姆斯壯（M.A.Armstrong）

書籍目錄

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

章節(jié)摘錄

版權(quán)頁：插圖：

編輯推薦

《群與對稱(英文版)》是由世界圖書出版公司出版的。

圖書封面

圖書標(biāo)簽Tags

無

評論、評分、閱讀與下載

---

    群與對稱 PDF格式下載

---