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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Kazhdan groups with infinite outer automorphism group


Authors: Yann Ollivier and Daniel T. Wise
Journal: Trans. Amer. Math. Soc. 359 (2007), 1959-1976
MSC (2000): Primary 20F28, 20F06, 20E22, 20P05
Published electronically: November 17, 2006
MathSciNet review: 2276608
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Abstract | References | Similar Articles | Additional Information

Abstract: For each countable group $ Q$ we produce a short exact sequence $ 1\rightarrow N \rightarrow G \rightarrow Q\rightarrow 1$ where $ G$ has a graphical $ \frac16$ presentation and $ N$ is f.g. and satisfies property $ T$.

As a consequence we produce a group $ N$ with property $ T$ such that $ \operatorname{Out}(N)$ is infinite.

Using the tools developed we are also able to produce examples of non-Hopfian and non-coHopfian groups with property $ T$.

One of our main tools is the use of random groups to achieve certain properties.


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Additional Information

Yann Ollivier
Affiliation: CNRS, UMPA, École normale supérieure de Lyon, 46, allée d’Italie, 69364 Lyon cedex 7, France
Email: yann.ollivier@umpa.ens-lyon.fr

Daniel T. Wise
Affiliation: Department of Mathematics, McGill University, Montréal, Québec, Canada H3A 2K6
Email: wise@math.mcgill.ca

DOI: http://dx.doi.org/10.1090/S0002-9947-06-03941-9
PII: S 0002-9947(06)03941-9
Keywords: Outer automorphism groups, property $T$, small cancellation, random groups
Received by editor(s): September 27, 2004
Received by editor(s) in revised form: January 10, 2005
Published electronically: November 17, 2006
Additional Notes: This research was partially supported by NSERC grant
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.