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Date: Fri, 13 Oct 1995 15:01:31 -0400 (EDT)
From: "Jerry Bryan"
To: "Dan Hoey" ,
Subject: Re: Using 5 Generators
In-Reply-To: Message of 10/11/95 at 22:56:15 from hoey@aic.nrl.navy.mil
On 10/11/95 at 22:56:15 hoey@aic.nrl.navy.mil said:
>[in Q2]
>> The four rotations are i, b, bb, and bbb, where we use lower case
>> letters to simulate Frey and Singmaster's script notation for rotations.
>> For example, b is the whole cube rotation consisting of grasping
>> the Back face and rotating the whole cube (not just the Back face)
>> clockwise by 90 degrees.
>The reflections are similarly rrv, rrbv, ttv, and ttbv, where t and r
>are the whole-cube rotations by the Top and Right faces, and v is the
>central inversion.
I am not quite sure why it took me so long to figure out that
Q2-conjugation was the appropriate symmetry when generating G
without B and B'. With the wisdom if hindsight, it is perhaps
because the Q2 subgroup of M could be described as fixing the
B and F face centers, and I was thinking only in terms of fixing
the B face center. Obviously, you cannot fix the B face center
without also fixing the F face center. Thus, it is clear that
Q2-conjugation is also the appropriate symmetry when generating
G without F and F'.
Q1 and Q3 are subgroups of M which are conjugate with Q2 in Dan's
taxonomy of subgroups of M. Q1 fixes the T and D face centers, and
would be the appropriate symmetry when generating G without T and T',
or without D and D'. Q3 fixes the R and L face centers, and would be
the appropriate symmetry when generating G without R and R', or without
L and L'.
= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
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