In three dimensions, I know that in general rotations on the unit sphere are non-commutative, but I was wondering if there is a subset/subgroup of rotations that *are* commutative, and what this type of set/group looks like. Again, I'm interested in rotations that satisfy
$$R\_1 R\_2 - R\_2 R\_1=0$$
for the unit sphere in $\mathbb{R}^3$. Then if such a set exists, would such a set/group exist for the surface $|x|^2+|y|^2+|z|^2=1$, in $\mathbb{C}^3$?

Thanks,