TL;DRAbstract
Chapter 3 is an introduction to group theory, emphasizing permutations, group actions, orbits, and symmetry. The symmetry of classical objects is considered via group actions as encoded by the Cayley graph. Also classical geometric groups are introduced as key examples, such as the wallpaper groups. The chapter leads up to and concludes with a computation of the outer automorphism group of the symmetric group on six elements as represented by an action on antipodally symmetric colorings of the edges of an icosahedron, a method inspired by a construction of Coxeter.
Chat with Paper
AI Agents for this Paper
Chapter 3 is an introduction to group theory, emphasizing permutations, group actions, orbits, and symmetry. The symmetry of classical objects is considered via group actions as encoded by the Cayley graph. Also classical geometric groups are introduced as key examples, such as the wallpaper groups. The chapter leads up to and concludes with a computation of the outer automorphism group of the symmetric group on six elements as represented by an action on antipodally symmetric colorings of the edges of an icosahedron, a method inspired by a construction of Coxeter.
Keywords
Chat
Click to start Chat