  Let $k$ be an algebraically closed field of prime characteristic $p$, and let
$P$ be a $p$-subgroup of a finite group $G$. We give sufficient conditions for
the $kG$-Scott module $\mathrm{Sc}(G,P)$ with vertex $P$ to remain
indcomposable under the Brauer construction with respect to any subgroup of
$P$. This generalizes similar results for the case where $P$ is abelian. The
background motivation for this note is the fact that the Brauer
indecomposability of a $p$-permutation bimodule is a key step towards showing
that the module under consideration induces a stable equivalence of Morita
type, which then may possibly be lifted to a derived equivalence.
