Jonas Deré (KU Leuven) : Strongly scale-invariant virtually polycyclic groups

A finitely generated group is called strongly scale-invariant if there exists an injective endomorphism on the group with image of finite index and such that the intersection of the images of the iterations is trivial. The only known examples of such groups are virtually nilpotent, or equivalently, all examples have polynomial growth. A question by Nekrashevych and Pete asks whether these groups are the only possibilities for such endomorphisms, motivated by the positive answer due to Gromov in the special case of expanding group morphisms. In this talk, we will discuss this question in the special case of virtually polycyclic groups, by using the algebraic hull of these groups.