The object of the research stay is to cooperate with the research group led by Wolfgang Kimmerle on finite subgroups of integral group rings.

The main question we are going to address is the Zassenhaus Conjecture that predicts that all the normalized torsion units of the integral group ring ZG of a finite group G are rationally conjugate of elements of G.

This is related to the Prime Graph Conjecture that claims that G and the group V(ZG) of normalized units of ZG have the same prime groups, and to the stronger conjecture that predicts that the orders of the torsion elements of G and V(ZG) are the same.

Another question that we want to address is whether the Sylow subgroups of G and V(ZG) are the rationally conjugate.