2 3 A pr 2 00 8 Groups with the same cohomology as their profinite completions

  • Karl Lorensen
  • Published 2008
For any positive integer n, An is the class of all groups G such that, for 0 ≤ i ≤ n, H i (ˆ G, A) ∼ = H i (G, A) for every finite discretê G-module A. We describe certain types of free products with amalgam and HNN extensions that are in some of the classes An. In addition, we investigate the residually finite groups in the class A2.