The abelian rank conjecture for homologically trivial group actions on 4-manifolds

Let $G$ be a finite group acting locally linearly and homologically trivially on a closed, simply connected $4$-manifold $X$, and suppose that $b_2(X)\ge 3$. Here, abelian of rank at most $2$ means that $G$ is an abelian group whose minimal number of generators is at most $2$.

Abelian rank conjecture. The group $G$ must be abelian of rank at most $2$.

This conjecture refines the preceding observation that, after removing pseudofreeness, elementary abelian groups such as $C_p\times C_p$ can act homologically trivially on standard $4$-manifolds. Its status is not resolved in the supplied source.