## is there a closed normal maximal subgroup in a connected linear algebraic group ?

Let G be a connected linear algebraic group. is there a unique closed normal maximal subgroup in G ?

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 of course not: in $PSL_2\times PSL_2$ (in the place of $PSL_2$ you may insert any simple group) for example you have at least two closed maximal normal subgroups – zroslav Jun 15 2011 at 19:11 No. Try $G = \mathbf{G}_a^2$ over $\mathbf{C}$, say. – Konstantin Ardakov Jun 15 2011 at 19:11 Or $C^*$ which has no maximal subgroups closed subgroups! – Bugs Bunny Jun 15 2011 at 21:25 Please see the "how to ask" page before asking another question. – S. Carnahan♦ Jun 16 2011 at 5:26