  Given a profinite group G of finite p-cohomological dimension and a pro-p
quotient H of G by a closed normal subgroup N, we study the filtration on the
Iwasawa cohomology of N by powers of the augmentation ideal in the group
algebra of H. We show that the graded pieces are related to the cohomology of G
via analogues of Bockstein maps for the powers of the augmentation ideal. For
certain groups H, we relate the values of these generalized Bockstein maps to
Massey products relative to a restricted class of defining systems depending on
H. We apply our study to prove lower bounds on the p-ranks of class groups of
certain nonabelian extensions of the rational numbers and to give a new proof
of the vanishing of triple Massey products in Galois cohomology.
