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Speaker: Andrzej Szczepański (University of Gdańsk)

Title: Symmetries of Crystallographic Groups

Abstract:

This is joint work with R.Lutowski.

Let \(\Gamma\) be a crystallographic group of dimension \(n\), i.e. a discrete, cocompact subgroup of Isom\((R^n) = O(n) \ltimes R^n\). By symmetries of \(\Gamma\) we understand a group of its outer automorphisms. For any \(n \geq 2\), we shall construct a crystallographic group with trivial center and a trivial outer automorphism group. Moreover, we shall present properties of an example (constructed in Aachen by R. Waldmüller in 2003 under advice of Gerhard) of the torsion free crystallographic group of dimension 141 with a trivial center and a trivial outer automorphism group.