Residuele eindigheidsgroei voor virtuele minimaxgroepen

The residual finiteness growth is a function that tries to capture to what extent a residually finite (finite generated) group is residually finite. The extent is given by the asymptotic behaviour of the function. Concretely we can find a homomorphism to a finite group for each non-trivial group element such that its image is also non-trivial. The residual finiteness growth gives an estimate of the minimal number of elements in that finite group based on the word norm or word length of the original group element. We aim to find this function for different classes of groups. More specifically, we focus on finitely generated, residually finite, virtually minimax groups. We establish, in particular, exact asymptotics for all virtually nilpotent groups. Also, we improve the known bounds for polycyclic groups.