The lower-order finite p-group cycle map conjecture

Let $p$ be a prime number and let $K$ be a finite $p$-group of order less than $p^{p+3}$. The mod $p$ cycle map

$$cl:CH^2BK/p\to H^4(BK)$$

Cycle map conjecture. The map $cl$ is injective.

This conjecture proposes that the smallest finite $p$-groups for which the mod $p$ cycle map fails to be injective have order at least $p^{p+3}$. The paper establishes non-injectivity for a group of order $p^{p+3}$, while the asserted lower bound remains open.