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November 24th, 2016, 10:37 PM   #1
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Showing that an action of a group on a set is proper

Let X represent the set = {1,2,3,4,5,6,7,8}
Then the elements of the symmetry group (Dihedral Group- D8 ) permute the elements of the set.

How do I show that the action of D8 on the set is proper?

I understand that the group G must be a topological group (which is continuous) and so it must therefore be infinite.

What I am stuck on is that the group is not infinite.

I have used this website but I am unsure of what I am doing wrong.

Thank you for reading.
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