1. The problem statement, all variables and given/known data Let G be a discrete group in which every element is orientation-preserving. Prove that the point group G' is a cyclic group of rotations and that there is a point p in the plane such that the set of group elements which fix p is isomorphic to G' 3. The attempt at a solution Ok since every element of the group is orientation-preserving, we know that there are only translations and rotations. so every element of G can be written as tarhotheta. and phi: G----> O So the point group G' = phi(G) = rhotheta Im guessing i have to use the fixed point theorem for the second part, but i have no clue how to do that. Any help is appreciated.