Groups with the same cohomology as their profinite completions

For any positive integer n, A(n) is the class of all groups G such that, for 0 <= i <= n, H-i(((G) over cap, A) congruent to H-i (G, A) for every finite discrete (G) over cap -module A. We describe certain types of free products with amalgam and HNN extensions that are in some of the classes A(n). In addition, we investigate the residually finite groups in the class A(2). (c) 2008 Elsevier Inc. All rights reserved.