CHAPTER 1 Symmetries of the Tetrahedron 1
CHAPTER 2 Axioms 6
CHAPTER 3 Numbers 11
CHAPTER 4 Dihedral Groups 15
CHAPTER 5 Subgroups and Generators 20
CHAPTER 6 Permutations 26
CHAPTER 7 Isomorphisms 32
CHAPTER 8 Plato's Solids and Cayley's Theorem 37
CHAPTER 9 Matrix Groups 44
CHAPTER 10 Products 52
CHAPTER 11 Lagrange's Theorem 57
CHAPTER 12 Partitions 61
CHAPTER 13 Cauchy's Theorem 68
CHAPTER 14 Conjugacy 73
CHAPTER 15 Quotient Groups 79
CHAPTER 16 Homomorphisms 86
CHAPTER 17 Actions,Orbits,and Stabilizers 91
CHAPTER 18 Counting Orbits 98
CHAPTER 19 Finite Rotation Groups 104
CHAPTER 20 The Sylow Theorems 113
CHAPTER 21 Finitely Generated Abelian Groups 119
CHAPTER 22 Row and Column Operations 125
CHAPTER 23 Automorphisms 131
CHAPTER 24 The Euclidean Group 136
CHAPTER 25 Lattices and Point Groups 145
CHAPTER 26 Wallpaper Patterns 155
CHAPTER 27 Free Groups and Presentations 166
CHAPTER 28 Trees and the Nielsen-Schreier Theorem 173
Bibliography 181
Index 183