Finitely presentable, non-Hopfian groups with Kazhdan's Property (T) and infinite outer automorphism group

Details Finitely presentable, non-Hopfian groups with Kazhdan's Property (T) and infinite outer automorphism group Finitely presentable, non-Hopfian groups with Kazhdan's Property (T) and infinite outer automorphism group

2005-02-07

arxiv.org/abs/math/0502140v3

Proc. Amer. Math. Soc. 135, 951-959, 2007

Mathematics

Group Theory

8 pages, no figure. To appear in Proc. Amer. Math. Soc

Scientific paper

10.1090/S0002-9939-06-08588-1

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.

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