  The Hilbert-Smith Conjecture states that if G is a locally compact group
which acts effectively on a connected manifold as a topological transformation
group, then G is a Lie group. A rather straightforward proof of this conjecture
is given. The motivation is work of Cernavskii (``Finite-to-one mappings of
manifolds'', Trans. of Math. Sk. 65 (107), 1964.) His work is generalized to
the orbit map of an effective action of a p-adic group on compact connected
n-manifolds with the aid of some new ideas. There is no attempt to use Smith
Theory even though there may be similarities.
  It is well known that if a locally compact group acts effectively on a
connected n-manifold M and G is not a Lie group, then there is a subgroup H of
G isomorphic to a p-adic group A_p which acts effectively on M. It can be shown
that A_p can not act effectively on an n-manifold and, hence, The Hilbert Smith
Conjecture is true. The existence of a non empty fixed point set adds some
complexity to the proof. In this paper, it is shown that A_p can not act freely
on a compact connected n-manifold. The basic ideas for the general case are
more clearly seen in this case. The general proof will be given in another
paper.
