Pro-p Galois groups of rank≥4

Let p be a prime > 2, let F be a field of characteristic not equal p containing a primitive p-th root of unity and let G(F)(p) be the Galois group of the maximal Galois-p-extension of F. If rkG(F)(p) less than or equal to 4 then G(F)(p) is, free pro-p product of metabelian groups or G(F)(p) is a Demuskin group of rank 4.