Characterisation of Q-rank 1 I'm looking for a reference and/or the original source for the following fact:
An irreducible non-uniform lattice in a semisimple Lie group without compact factor has Q-rank 1 if and only if it does not contain a subgroup isomorphic to a finite index subgroup of $SL(3,{\Bbb Z})$ or $SO(2,3)_{\Bbb Z}$.
 A: The proof of Kazhdan's property (T) for real simple Lie groups of real rank at least two as given in the old Bourbaki talk of Kirilllov and Delaroche involves showing (property (T) for $H=SL_3({\mathbb R}), Sp_2({\mathbb R})$ and then showing) that any such $G$ contains a subgroup locally isomorphic to $H$. 
Exactly the same proof shows that any $\mathbb Q$-simple linear algebraic group $G$ of $\mathbb Q$ rank at least two  contains a subgroup locally $\mathbb Q$-isomorphic to $SL_3$ or to $Sp_2$. 
In detail, such a $G$ contains a subgroup $G_0$ which is $split$ over $\mathbb Q$ and of the same $\mathbb Q$-rank as $G$. By looking at the Dynkin diagram  of $G_0$, one can extract a sub-diagram of type $A_2$ or $B_2$ except for $G_2$ where this (i.e. that $G_2$ contains $A_2$, the root system of short roots in the root system of $G_2$)  can be proved directly by looking at its root system. 
[Edit] Misha (in the comments) was right; this result that any $k$-simple group of $k$-rank at least two contains a subgroup locally isomorphic to $SL_3$ or $Sp_4$) is explicitly stated and proved in Margulis' book; see Proposition (1.6.2) of Margulis' book titled  " Discrete subgroups of Semi-simple Lie groups (Ergbnisse tract, volume 17)". The result about arithmetic groups can be deduced from this by taking $k={\mathbb Q}$. 
