The weak Hilbert–Smith conjecture for free proper actions

Let $G$ be a locally compact group acting freely and properly on a connected finite-dimensional topological manifold $M$ such that the orbit space $M/G$ is finite dimensional.

Weak Hilbert–Smith conjecture. $G$ is a Lie group.

This is a weaker form of the Hilbert–Smith conjecture, obtained by assuming that the action is free and proper and that the orbit space is finite dimensional. Its status is not resolved in the source.