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Topic: "Unphysical" symmetries
Replies: 5   Last Post: Dec 18, 2013 12:03 PM

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Jose Carlos Santos

Posts: 4,896
Registered: 12/4/04
Re: "Unphysical" symmetries
Posted: Dec 8, 2013 10:23 AM
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On 08/12/2013 13:38, wrote:

> Example: The symmetry group of the utility graph K3,3 has 72 elements
> if I googled correctly. So no 3D symmetry group fits.
> If I go to higher symmetry, is *any* group the subgroup
> of some R_n (rotation group of dimension n)? Methinks yes,
> but already in 4D my head hurts :-)

I am not sure to have understood your question, but if you are asking
"Is every finite group isomorphic to a subgroup of the group SO(R,n) of
all orientation-preserving linear isometries of R^n, for some _n_?",
then yes, it is true. Do you want a proof of this?

Best regards,

Jose Carlos Santos

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