[next] [prev] [up] Date: Mon, 02 Jan 95 23:00:01 -0500 (EST)
[next] [prev] [up] From: Jerry Bryan <BRYAN@wvnvm.wvnet.edu >
[next] [prev] [up] Subject: Re: Normal Subgroups of G

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.

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