In the group of Möbius maps, what is the order of the Möbius map ? What is the order of the Möbius map ?
Prove that every Möbius map is conjugate either to a map of the form (some ) or to the . Is conjugate to a map of the form
Let be a Möbius map of order , for some positive integer . Under the action on of the group generated by , what are the various sizes of the orbits? Justify your answer.