Rubik's Group Question - Commutators
Suppose that $f: G \rightarrow S_C$ be the action of Rubik's group $G$ on
the collection of $C$ of corner cubelets. So if $C_1$ and $C_2$ be
distinct corner cubelets. Show that there is a move $M \in G$ which maps
FRU (front right up) to $C_1$ and FRD (front right down) to $C_2$. Then
find a move $N$ in rubiks group $G$ which exchanges the cubelets FRU and
FRD but leaves all the other corner cubelets in their place.
I am really lost on the first part of this problem. And I think for the
second part, I must find a commutators in order to leave the other corner
cubelets in one place with just exchanging FRU and FRD. Any help would be
appreciated.
