Bogomolov's vanishing conjecture for finite simple groups

Let $G$ be a finite simple group. The unramified cohomology group $H^2_{\rm nr}(G)$ is identified with the Bogomolov multiplier $B_0(G)$.

Bogomolov's conjecture.

$$H^2_{\rm nr}(G)=B_0(G)=0.$$

This conjecture asserts that finite simple groups do not produce nontrivial degree-two birational invariants. It is presented as a particular case of the broader hypothesis that all nonramified cohomology of finite simple groups is trivial; its resolution status is not specified in the source.