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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...
The set of all Abelian simply transitive subgroups of the affine group naturally
corresponds to the set of real solutions of a system of algebraic equations. We classify
all simply transitive subgroups of the symplectic affine group by constructing a model
space for the corresponding variety of solutions. Similarly, we classify the
complete global model spaces for flat special Kähler manifolds with a constant cubic form.
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