On the structure of the ring of continuous functions on spaces with p-Adic group of transformations

The interest to p-Adic groups actions on topological spaces, especially on manifolds, is arisen from the well-known Hilbert–Smith problem: is any action of such groups on compact manifolds non-effective? that is, does there exist an element of the group other than unit which fixes all elements of the space? In the present paper we develop new techniques for study the structure of the ring of continuous functions on spaces with p-Adic group action, based on integration along the orbits, and give some its applications. The text is a widened version of a part of the talk presented by the author on the 2010 International Conference on Topology and its Applications (Nafpactos, Greece, June 26–30, 2010) [14].