ON LOCALLY LIPSCHITZ LOCALLY COMPACT TRANSFORMATION GROUPS OF MANIFOLDS

In this paper we show that a "locally Lipschitz" locally compact transformation group acting continuously and effectively on a connected paracompact locally Euclidean topological manifold is a Lie group. This is a contribution to the proof of the Hilbert-Smith conjecture. It generalizes the classical Bochner-Montgomery-Kuranishi Theorem[1, 9] and also the Re-povs-Scepin Theorem [17] which holds only for Riemannian manifolds.