Compact group acti̇ons on solenoi̇dal spaces

In this work we studied finite sheeted covering maps on the Solenoidal Spaces, principal fiber bundle structure of p-adic Solenoid over S^1 and looking in the opposite direction it was shown that, under certain conditions, one way to obtain compact finite dimensional manifolds with effective p-adic actions. Since such a manifold has not yet been found, this is not a counter example to the Hilbert-Smith conjecture. On the other hand these conditions are about equivariance and higher homotopy groups. However, using the fact that Hilbert-Smith conjecture is true for 3-dimensional case, it was shown that there is no Z_P-equivariant map between 3-spheres.