Recent content by fronton

I am sorry please ignore my previous post. I didn't read Vargo's reply which proves very nicely what I had set out to prove,

Thanks everybody for the clarification. You're right I did forget about reflections. But just merely out of mathematical curiosity is there a way to prove for isometries involving rotations only, not involving reflections, that only a single point is fixed for all rotations of a finite group...

There is a theorem for finite groups of isometries in a plane which says that there is a point in the plane fixed by every element in the group (theorem 6.4.7 in Algebra - M Artin). While the proof itself is fairly simple to understand, there is an unstated belief that this is the only point...