Kazhdan groups with infinite outer automorphism group

Details Kazhdan groups with infinite outer automorphism group Kazhdan groups with infinite outer automorphism group

2004-09-13

arxiv.org/abs/math/0409203v1

Mathematics

Group Theory

18 pages

Scientific paper

For each countable group $Q$ we produce a short exact sequence $1\to N \to G \to Q\to 1$ where $G$ is f.g. and 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 $\Out(N)$ is infinite. Using the tools developed we are also able to produce examples of nonHopfian 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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