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: smartta 时间: 2011-8-24 15:38 标题: 群与对称:英文(影印版)