  We consider the p-Zassenhaus filtration (G_n) of a profinite group G. Suppose
that G=S/N for a free profinite group S and a normal subgroup N of S contained
in S_n. Under a cohomological assumption on the n-fold Massey products (which
holds e.g., if the p-cohomological dimension of G is at most 1), we prove that
G_{n+1} is the intersection of all kernels of upper-triangular unipotent
(n+1)-dimensional representations of G over \mathbb F_p. This extends earlier
results by Minac, Spira, and the author on the structure of absolute Galois
groups of fields.
