(adsbygoogle = window.adsbygoogle || []).push({}); 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 t_{a}rho_{theta}.

and phi: G----> O

So the point group G' = phi(G) = rho_{theta}

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.

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# Homework Help: Proving there is a fixed point in a discrete group of rotations

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