P-adic Nori Theory

Given a fixed integer n, we consider closed subgroups G of H = GL(n,Z_p) where Z_p denotes the ring of p-adic integers and p is sufficiently large in terms of n. Assuming that the Zariski closure of G has no toric part, we give a condition on the (mod p) reduction of G which guarantees that G is of bounded index in its Zariski closure in H.