On torsion subgroups in integral group rings of finite groups

The object of this article are torsion subgroups of the normalized unit group V(ZG) of the integral group ring ZG of a finite group G. For specific subgroups W we study the Gruenberg–Kegel graph Π(W). It is shown that the central elements of an isolated subgroup U of a group basis H of ZG are the normalized units of its centralizer ring CZG(U). Moreover Π(NV(ZG)(U))=Π(NH(U)). If G has elementary abelian Sylow 2-subgroups of order at most 8 each finite 2-subgroup of V(ZG) is rationally conjugate to a subgroup of G. Finally torsion subgroups of V(ZG) in the case when G is a minimal simple group are considered. It follows that if G is a simple group which admits a non-trivial partition for each prime p the p-rank of a torsion subgroup of V(ZG) is bounded by that one of G.