# Groups with the same cohomology as their profinite completions - Mathematics > Group Theory

Abstract: For any positive integer $n$, $\mathcal{A} n$ is the class of all groups $G$such that, for $0\leq i\leq n$, $H^i\hat{G},A\cong H^iG,A$ for every finitediscrete $\hat{G}$-module $A$. We describe certain types of free products withamalgam and HNN extensions that are in some of the classes $\mathcal{A} n$. Inaddition, we investigate the residually finite groups in the class$\mathcal{A} 2$.

Author: Karl Lorensen

Source: https://arxiv.org/