Generators of simple Lie algebras and the lower rank of some pro-p groups

Let g be a simple classical Lie algebra over a field IT of characteristic p > 7. We show that > d(g) = 2, where d(g) is the number of generators of g. Let G be a profinite group. We say that G has lower rank less than or equal to l, if there are {G(alpha)} open subgroups which form a base for the topology at the identity and each G(alpha) is generated (topologically) by no more than 1 elements. There is a standard way to associate a Lie algebra L(G) to a finitely generated (filtered) pro-p group G. Suppose L(G) congruent to g circle times tF(p)[t], where q is a simple Lie algebra over F-p, the field of p elements. We show that the lower rank of G is less than or equal to d(g) + 1. We also show that if g is simple classical of rank r and p > 7 or p > 2r(2) - r, then the lower rank is actually 2.