PIMS - ULethbridge Distinguished Speaker: Francesco Pappalardi

We shall start by outlining some aspects of the long history of the Artin Conjecture. Then we shall consider a multiplicative subgroup G of Q*. If p is a prime for which the valuation v_p(x) = 0 for every x in G, then the group G_p ={x (mod p): x is in G} is a well defined subgroup of F_p. We will consider various properties of G_p as p varies and propose various new results in analogy with the old Artin Conjecture for Primitive roots.