Unstable Adams operation conjecture for finite p-groups

Let $G$ be a finite $p$-group, let $E$ be a $p$-complete complex-oriented spectrum with associated formal group of height $n$, and let $E^2(f)$ denote the induced map in degree-two $E$-cohomology. An unstable Adams operation of degree $p$ is a self-map $f:BG\to BG$ compatible up to homotopy with the degree-$p$ operation on $B(G/G')$, where $G'$ is the commutator subgroup. Unstable Adams operation conjecture. There is an unstable Adams operation $f:BG\to BG$ of degree $p$ such that, on the two-dimensional Euler classes $x$, the induced map has the power-series expansion

$$E^2(f)(x)=v_0x+v_1x^p+\cdots.$$

Such operations would provide a way to study roots of $p^j$-series in generalized Tate constructions for non-abelian groups. The supplied text gives no resolution status or supporting evidence beyond presenting this assertion as a conjectural tool.