On the normalizer problem

In this paper the normalizer problem of an integral group ring of an arbitrary group G is investigated. It is shown that any element of the normalizer N-u1(G) of G in the group of normalized units u(1)(ZG) is determined by a finite normal subgroup. This reduction to finite normal subgroups implies that the normalizer property holds for many classes of (infinite) groups, such as groups without non-trivial 2-torsion, torsion groups with a normal Sylow 2-subgroup, and locally nilpotent groups. Further it is shown that the commutator of N-u1(G) equals G' and N-u1(G)/G is finitely generated if the torsion subgroup of the finite conjugacy group of G is finite. (C) 2002 Elsevier Science.