Archives

In QTM, the whole cube is generated using U,D,R,L,F,B moves.
If we drop some moves we end up with some subgroups. The subgroups are:

1) I [the identity]
2) U  
3) U,D
4) U,F
5) U,D,F
6) U,F,R
7) U,D,F,B
8) U,D,F,R
9) U,D,F,B,R

I know the depth table for subgroups 1) 2) 3) and 4):
The subgroup 1) generated by "no move", has the following obvious table:

Moves Deep       arrangements (q only)     

  0                    1                   
                   ------
                       1

The subgroup 2) generated only by the move U, has the following table: