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.