I've been trying to find this but I have no luck!
One possibility is to think of it as a group (abstract algebra).
this might help:
Think of what as a group? What are the elements, what is the group operation?
You can think of the twists as the elements of your group, the group operation is just the natural composition of these transformations, with sequences of transformations leading to the same cube position being identified. Each basic twist is an element of order 4 for example, twists of opposing faces commute, etc.
Plenty of hits come up in google under 'mathematics rubik's cube'.
Separate names with a comma.