Let $G$ denotes an infinite coutable discrete group with Kazhdan's property (T),
My question is:
is it known that the 2nd cohomology group $H^2(G,\mathbb{Z}G)$ is torsion free?
Thanks in advance!
Note that for any finitely presented group $G$, $H^2(G,\mathbb{Z}G)$ is always torsion-free by proposition 13.7.1 in GTM 243(Topological methods in group theory).