Let $\Gamma$ be a discrete group, and $V$ a (not necessarily finite-dimensional) $\mathbb{Q}_p[\Gamma]$-module. I am looking for general criteria that ensure that $H^2(\Gamma, V) = 0$.
The simplest example is with $\Gamma$ free or finite. Using the Hochschild-Serre spectral sequence, one can also show that this is true when $\Gamma$ is virtually free. Are there any other interesting examples?
I am particularly interested in finitely presented examples.