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

de Cornulier, Yves

doi:10.1090/S0002-9939-06-08588-1

Finitely presentable, non-Hopfian groups with Kazhdan’s Property (T) and infinite outer automorphism group
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by Yves de Cornulier PDF

Proc. Amer. Math. Soc. 135 (2007), 951-959 Request permission

Erratum: Proc. Amer. Math. Soc. 139 (2011), 383-384.

Abstract:

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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