Central Configurations for NewtonianN+2p+1-Body Problems

We show the existence of spatial central configurations for the N+2p+1-body problems. In the N+2p+1-body problems, N bodies are at the vertices of a regular N-gon T ; 2p bodies are symmetric with respect to the center of T, and located on the straight line which is perpendicular to the regular N-gon T and passes through the center of T; the N+2p+1th is located at the the center of T. The masses located on the vertices of the regular N-gon are assumed to be equal; the masses located on the same line and symmetric with respect to the center of T are equal