Finitely presentable, non-Hopfian groups with Kazhdan's Property (T) and   infinite outer automorphism group
  We give simple examples of Kazhdan groups with infinite outer automorphism groups. This answers a question of Paulin, independently answered by Ollivier and Wise by completely different methods. As arithmetic lattices in (non-semisimple) Lie groups, our examples are in addition finitely presented.   We also use results of Abels about compact presentability of p-adic groups to exhibit a finitely presented non-Hopfian Kazhdan group. This answers a question of Ollivier and Wise. 
Yves de Cornulier