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Finitely presentable, non-Hopfian groups with
Kazhdan's Property (T) and infinite
outer automorphism group
Author(s):
Yves
de Cornulier
Journal:
Proc. Amer. Math. Soc.
135
(2007),
951-959.
MSC (2000):
Primary 20F28;
Secondary 20G25, 17B56
Posted:
September 26, 2006
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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  -adic groups to exhibit a finitely presented non-Hopfian Kazhdan group. This answers a question of Ollivier and Wise.
References:
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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:
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
Posted:
September 26, 2006
Communicated by:
Dan M. Barbasch
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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