 The " unrestricted " version of Hilbert 's fifth problem , closer to Hilbert 's original formulation , considers both a locally Euclidean group G and another manifold M on which G has a continuous action . Hilbert asked whether , in this case , M and the action of G could be given a real analytic structure . It was quickly realized that the answer was negative , after which attention centered on the restricted problem . However , with some additional smoothness assumptions on G and M , it might yet be possible to prove the existence of a real analytic structure on the group action . The Hilbert – Smith conjecture , still unsolved , encapsulates the remaining difficulties of this case . 
