內容簡介

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.
 

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

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