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It is well known that if we define G=<Q> for the twelve quarter turns

q in Q, we can also generate G as G=<F,U,L,R,D>, leaving out B and B'.

Leaving out any other quarter turn would do as well, but I

am going to stick to leaving out B for illustrative purposes.

However, when one of the quarter turns is left out, the length of most

positions will change. In particular, we will no longer have |B|=1.

My reading of the archives indicates that we do not know what the

length of B would be in this situation, nor what a minimal process

for B would be.

I am going to take a crack at this problem via exhaustive search.

But I like to use representative elements of conjugacy classes in

my searches, and I don't think I can do so in this situation.

For full-blown searches of G, I use M-conjugacy classes. For subsets

and/or restrictions of G, I use appropriate subsets and/or restrictions

of M. But I don't think I can use conjugacy classes at all for this

problem. The group is still G, even though lengths have changed, so

no subset and/or restriction of M is appropriate. But when G is

generated as <F,U,L,R,D>, we do not necessarily have |X|=|m'Xm|

for all m in M.

Am I missing something obvious? I don't think so, but in the

meantime I am going to have to start the search without conjugacy

classes. Bummer.

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 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