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On 12/30/94 at 15:17:00 Martin Schoenert said:

>Basically the same argument works for GE. But there is one exception.

>Namely VE has one normal subgroup of size 2 , generated by the element

>(1,1,...,1;<identity>). You may not recognize this element, but it is

>in fact the superflip, which flips all twelve edges. I shall call this

>subgroup Z.

Thus GE has 5 normal subgroups GE, GE', VE, Z, and <1>.

I am still absorbing this article, which exceeds my current

knowledge of group theory. But at the risk of asking a dumb

question, doesn't the center of GE (and of G) in fact consist

of more than just the Superflip and the identity? Does it

not also include the Pons Asinorum and the composition of

the Pons Asinorum and the Superflip? Call the Pons Asinorum P

and the Superflip E. I think you are saying Z={I,E}. But

isn't the center {I,P,E,PE}, with subgroups {I,P}, {I,E},

{I,PE}, and {I}? These should all be central, and hence

also normal, I would think.

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = Robert G. Bryan (Jerry Bryan) (304) 293-5192 Associate Director, WVNET (304) 293-5540 fax 837 Chestnut Ridge Road BRYAN@WVNVM Morgantown, WV 26505 BRYAN@WVNVM.WVNET.EDU