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SNOOTCHIEBOOCHEE
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Homework Statement
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'
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.