It was noted that the Laguerre group is indeed isomorphic to the Lorentz group (or the Poincaré group if translations are included), as both groups leave invariant the form d x 1 2 + d x 2 2 + d x 3 2 − − d x 4 2 . After the first comparison of the Lorentz transformation and the Laguerre inversion by Bateman (1910) as mentioned above, the equivalence of both groups was pointed out by Cartan in 1912 and 1914, and he expanded upon it in 1915 (published 1955) in the French version of Klein's encyclopedia. Also Poincaré (1912, published 1921) wrote: