Profinite modules of finite projective p-dimension

Let G be a profinite group, p a prime number and A a profinite -module of finite projective p-dimension pdG,p(A). Let N be a closed normal subgroup of G such that N is of finite cohomological p-dimension cdp(N), is nonzero and finite for k=min{cdp(N),pdG,p(A)} and N acts trivially on A. Then the virtual projective p-dimension vpdG/N,p(A) of A as a -module is finite and vpdG/N,p(A)=pdG,p(A)−k. In the case when this generalizes the main result from [Th. Weigel, P.A. Zalesskii, Profinite groups of finite cohomological dimension, C. R. Acad. Sci. Paris Sér. I 338 (2004) 353–358].