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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Author: Yves de Cornulier
Journal: Proc. Amer. Math. Soc. 135 (2007), 951-959
MSC (2000): Primary 20F28; Secondary 20G25, 17B56
Published electronically: September 26, 2006
Erratum: Proc. Amer. Math. Soc. 139 (2011), 383-384
MathSciNet review: 2262894
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

Yves de Cornulier
Affiliation: Institut de Géométrie, Algèbre et Topologie (IGAT), École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
Email: decornul@clipper.ens.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08588-1
PII: S 0002-9939(06)08588-1
Received by editor(s): February 25, 2005
Received by editor(s) in revised form: October 28, 2005
Published electronically: September 26, 2006
Communicated by: Dan M. Barbasch
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.