On locally Lipschitz locally compact transformation groups of manifolds

M. A. George

Address. Department of Mathematics, Voorhees College, Denmark, SC 29042, U.S.A.

E-mail: adelgeorge1@yahoo.com

Abstract. 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 Repov\v{s}-\v{S}\v{c}epin Theorem [17] which holds only for Riemannian manifolds.

AMSclassification. Primary 57S05, Secondary 54H15.

Keywords. Locally Lipschitz transformation group, Hilbert-Smith conjecture.