Stacked central configurations for Newtonian N+2pN+2p-body problems

We show the existence of spatial central configurations for the N+2pN+2p-body problems. In such a configuration, NN bodies are at the vertices of a regular NN-gon TT; 2p2p bodies are symmetric with respect to the center of TT, and located on the straight line which is perpendicular to the regular NN-gon TT and passes through the center of TT. The masses located on the vertices of the regular NN-gon are assumed to be equal; the masses located on the same line and symmetric with respect to the center of TT are equal.