Diameter of a direct power of a finite group

Abstract: We present two conjectures concerning the diameter of a direct power of a finite group. The first conjecture states that the diameter of G^n with respect to any generating set is at most n(|G|-rank(G)); and the second one states that there exists a generating set A, of minimum size, for G^n such that the diameter of G^n with respect to A is at most n(|G|-rank(G)). We will establish evidence for each of the above mentioned conjectures.