Published online by Cambridge University Press: 20 November 2018
Let $G$ be an arbitrary group and let
$U$ be a subgroup of the normalized units in
$\mathbb{Z}G$. We show that if
$U$ contains
$G$ as a subgroup of finite index, then
$U\,=\,G$. This result can be used to give an alternative proof of a recent result of Marciniak and Sehgal on units in the integral group ring of a crystallographic group.