Shank–Wehlau–Broer conjecture on modular invariant rings

Let $G$ be a finite $p$-group acting linearly on a finite-dimensional vector space $V$ over a field of characteristic $p>0$. Set $S=\operatorname{Sym}V^*$ and let $S^G$ denote the invariant subring. Regard $S$ as an $S^G$-module.

Shank–Wehlau–Broer conjecture. If $S^G$ is a direct summand of $S$ as an $S^G$-module, then $S^G$ is a polynomial ring.

This conjecture concerns the converse to the fact that a polynomial invariant ring is a direct summand of its symmetric algebra. It is attributed to R. J. Shank and D. L. Wehlau, and was reformulated by A. Broer; the supplied text does not state whether it has been resolved.