Groups with the same cohomology as their pro-pp completions

For any prime pp and group GG, denote the pro-pp completion of GG by Gˆp. Let CC be the class of all groups GG such that, for each natural number nn and prime number pp, Hn(Gpˆ,Z/p)≅Hn(G,Z/p), where Z/pZ/p is viewed as a discrete, trivial Gˆp-module. In this article we identify certain kinds of groups that lie in CC. In particular, we show that right-angled Artin groups are in CC and that this class also contains some special types of free products with amalgamation.