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Automorphism groups of polycyclic-by-finite groups and arithmetic groups

Oliver Baues, Fritz Grunewald (2006)

Publications Mathématiques de l'IHÉS

We show that the outer automorphism group of a polycyclic-by-finite group is an arithmetic group. This result follows from a detailed structural analysis of the automorphism groups of such groups. We use an extended version of the theory of the algebraic hull functor initiated by Mostow. We thus make applicable refined methods from the theory of algebraic and arithmetic groups. We also construct examples of polycyclic-by-finite groups which have an automorphism group which does not contain an arithmetic...

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