  Let $\mathcal{L}$ be finite dimensional restricted Lie algebra over an
algebraically closed field $k$ of characteritic $p>3$. A finite dimensional
restricted $\mathcal{L}$-module $V$ is called Richardson if $V$ is faithful and
there exists a subspace $R$ of $\mathfrak{gl}(V)$ such that
$[\mathcal{L},R]\subseteq R$ and $\mathfrak{gl}(V)=\mathcal{L}\oplus R$, where
we identify $\mathcal{L}$ with its image in $\mathfrak{gl}(V)$. In this paper
we show that if $\mathcal{L}$ admits an irreducible Richardson module then it
is isomorphic (as a restricted Lie algebra) to the Lie algebra of a reductive
$k$-group.
