The Schur multiplier exponent conjecture for finite p-groups

Let $G$ be a finite $p$-group, where $p$ is prime. The Schur multiplier exponent conjecture.

$$\exp(H_2(G,\mathbb{Z}))\mid p\exp(G).$$

This conjecture strengthens the known bound suggested by the counterexamples to Schur's exponent problem, all of which satisfy the displayed divisibility. It is proved in the cited work for odd $p$-groups of nilpotency class at most $p^2-1$, but remains open for arbitrary finite $p$-groups.