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I'm new to algebaric groups, so please accept my apology in advance if I post crazy questions.

Let $G$ be a classical simple group over a finite field $GF(q)$ and $P$ a parabolic subgroup of $G$ stabilizing an isotropic subspace. Is the Borel subgroup of $G$ maximal soluble in $P$ and is there any maximal soluble subgroup in $P$ besides the Borel subgroup? Here by maximal soluble I mean a maximal one among soluble subgroups of $P$.

Any feedback is appreciated!

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You are allowed to post crazy questions, as long as someone can understand you enough to answer. =) – Patrick Da Silva Nov 24 '12 at 2:32
@PatrickDaSilva Hope someone understanding my question kindly answer it:-) – Binzhou Xia Nov 24 '12 at 3:47
If you ask the same question here and on mathoverflow, please give a link to the other page to avoid duplicated work by people not checking both pages! – j.p. Nov 25 '12 at 17:40
@jug Oh, sorry, I should give a link. Thanks for reminding me! – Binzhou Xia Nov 26 '12 at 2:59

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