I wrote:

? The key is that commutators are always odd permutations. So do the
? move that is an odd permutation of the edges, then use commutators.

But I *Meant*:

! The key observation is that commutators are always even
! permutations. So you to perform an odd permutation on edge, you
! should do the move that is an odd permutation of the edges, then use
! commutators.

Dan