Dear Members of Mathoverflow,

I am interested about a Fact (if it is right) of the structure of parabolic subgroups of finite classical algebraic groups:

Let G be a classical algebraic group over the finite field of order $r^{e}$, and let $ P \leq G $ denote a maximal parabolic subgroup of G.

We regard the unipotent radical of P: $ R:=R_{U}(P) = O_{r}(P) $. Is it true, that R is a minimal normal subgroup of P? (For P being a parabolic subgroup which is not a maximal in G, it is not true. If we regard the PSL(3,$r^{e}$) and a Borel subgroup.)

If it is right for the maximal parabolic subgroups of G, are there any Theorems or Propositions about that?

Thank you much for your Answers.

I am interested about a Fact (if it is right) of the structure of parabolic subgroups of finite classical algebraic groups:

Let $G$ be a classical algebraic group over the finite field of order $r^{e}$, and let $P \leq G$ denote a maximal parabolic subgroup of $G$.

We regard the unipotent radical of $P$ by $ R:=R_{U}(P) = O_{r}(P)$. Is it true, that $R$ is a minimal normal subgroup of $P$? (For $P$ being a parabolic subgroup which is not a maximal in $G$, it is not true. For example, let $G:=\operatorname{PSL}(3,r^{e})$ and take as $P$ a Borel subgroup.)

Is it correct for the maximal parabolic subgroups of $G$? Are there any Theorems or Propositions about that?