From:

~~~ Subject:

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