  In [14] Hemmer conjectures that the module of fixed points for the symmetric
group $\Sigma_m$ of a Specht module for $\Sigma_n$ (with $n>m$), over a field
of positive characteristic $p$, has a Specht series, when viewed as a
$\Sigma_{n-m}$-module. We provide a counterexample for each prime $p$. The
examples have the same form for $p\geq 5$ and we treat the cases $p=3$ and
$p=2$ separately.
