I am reading Jacques Tits' paper "Homomorphismes `abstraits' de groupes de Lie" and he seems to be making a claim that if you have a simply connected Lie group then the derived subgroup is always closed. I was just wondering if this statement was true or not. When I consulted with my supervisor he seemed to think that that was not true and this made me wonder if I was misreading the text in some way.



query about Jacques Tits' "Homorphismes `abstraits' de groupes de Lie"
This is true. The point is that the derived subgroup is the integral subgroup of the derived Lie algebra, therefore is a Lie subgroup (hence closed) if the group is simply connected. See Bourbaki, *Lie Groups and Lie Algebras*, ch. III, § 9, no. 2, Corollary of Prop. 4.


