Yüksek boyutlu kürelerin çarpımı üzerine serbest etkiler

A classical conjecture in the theory of transformation groups states that if G=(Z/p)^r acts freely on a product of k spheres S^(n_1)x... x S^(n_k), then r<=k. We prove a special case of this conjecture. We show that given positive integers k,l and G = (Z/p)^r, there is an integer N such that if G acts freely and cellularly on a CW-complex homotopy equivalent to S^(n_1)x... x S^(n_k) where n_i > N for all i and |n_i - n_j| < l for all i, j; then r<=k.