Call the primitive moves on the rubik's cube "R,L,U,D,F,B" for right, left, up, down, front, and back respectively.
Let us say that I have a permutation of the stickers on the cube written as a word in the primitive moves, e.g.
Is there a way to find the set of all equivalent words in the primitive moves (under a certain length)?
I imagine that it would be something like $\sigma H$ where $\sigma$ is the word you start with and $H$ is a subgroup of $\langle R,L,U,D,F,B\rangle$.
Unfortunately, it's been awhile since I've done anything with group theory, so any help would be much appreciated.