Contraction of O(3) to E(2) and to the cylindrical group, and contraction of
the O(3)-like little group to the E(2)-like little group. The correspondence
between E(2) and the E(2)-like little group is isomorphic but not identical.
The cylindrical group is identical to the E(2)-like little group. The
Lorentz-boost of the O(3)-like little group for a massive particle is the same
as the contraction of O(3) to the cylindrical group.