Tl;dr: I am trying to show intuitively that the set of Rubik's cube rotations forms a group. (I am not talking about literal rotation of the cube, but, of the edges.)
The group axioms it must follow are:
- Associativity: Three actions applied in the succesions (ab)c and a(bc) are same.
- Identity action
- Inverse action for any action in the group
The second and third are pretty easy to see. But, how do I see that Rubik's cube rotations are associative under composition?