all the related cubes 2x2, 3x3, 4x4, 5x5. For me the cube it is to group theory

(of a partcular type of group) what a slide rule is to real arithmetic. Even "laboratory"

might not be too stong a label for it.

For example it's immediately obvious how [tex] xy \neq yx [/tex]. If you turn the front of the cube

and then the right you get a very different set of faces than the right followed by front.

Also, you can discover marvelous "operators" (my terminology) by doing some random

series of twists (abc) followed by a particular twist (Z) then undoing the first

twists (via cba), that is: abcZcba where the letters stand for some particular oriented

twist. What happens is that most of the cube is unperturbed except for some

marvelous little permutation like a twisted corner in place or three swapped edges.

My solutions then consist of applying these "operators" in sequence by inspection

to see which one is "needed" next.

Alas however, I am not formally trained in group theory and I would like

to know: How would one go about using GT to develop a more effective

or efficient solution to something like Rubik's cube? I know it has been

done, but my question is very specifically: Can anyone explain to the group theory novice

(but Rubik's cube expert) how one would actually go about using GT to

devise (more) efficient solutions to such a puzzle?