群与对称

　　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.

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