Thank you all a lot, now I see that it is quite rare that $R_{U}(P)$ is a minimal normal subgroup of P. For the $PSL(n,q)$ for example it holds for the stabilizer of a minimal Flag $ 0 \lneq W \lneq V $, with dim W = 1 or dim W = dimV – 1. Regards

Now I think I understand the problem better and can move on with the research. Thank you a lot for your kind help.