群与对称

　　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

　　    《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.